Class 11 : Physics (In English) – Chapter 10: Thermal Properties of Matter

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On June 21, 2025

EXPLANATION & SUMMARY

🔷 EXPLANATION SECTION (≈1700 words)

🔵 1. Introduction
All materials absorb or release heat energy when their temperature changes. The study of how substances expand, contract, or change state with temperature is called Thermal Properties of Matter.
💡 Concept:
Heat is a form of energy that flows from a body at higher temperature to one at lower temperature until both reach thermal equilibrium.

🟢 2. Temperature and Heat
➡️ Temperature measures how hot or cold a body is and determines the direction of heat flow.
➡️ Heat is energy in transit due to a temperature difference.
✔️ SI unit of temperature: Kelvin (K)
✔️ SI unit of heat: Joule (J)
💡 Conversion:
°C + 273 = K
Example: 27°C = 27 + 273 = 300 K

🔴 3. Thermal Expansion
When a body is heated, its molecules move faster and further apart. This causes expansion in length, area, or volume.

✴️ (a) Linear Expansion
If a rod of initial length L₀ increases in length by ΔL for a temperature rise ΔT, then
➡️ ΔL = α L₀ ΔT
where α = coefficient of linear expansion (per °C).
💡 Final length:
L = L₀ (1 + αΔT)

✴️ (b) Areal Expansion
For area A₀, the increase in area with rise in temperature is
➡️ ΔA = β A₀ ΔT, where β ≈ 2α

✴️ (c) Cubical Expansion
For volume V₀, the increase in volume is
➡️ ΔV = γ V₀ ΔT, where γ ≈ 3α
✔️ For isotropic solids, γ = 3α

💡 Note: Expansion is proportional to temperature rise only for small ΔT. For large temperature changes, the relationship becomes nonlinear.

🟡 4. Anomalous Expansion of Water
When water is cooled from 4°C to 0°C, it expands instead of contracting.
The volume is minimum and density maximum at 4°C.
💧 This is vital for aquatic life — ice floats on water and insulates the lower layers from freezing.

🔵 5. Thermal Expansion in Everyday Life
✔️ Gaps are left between railway tracks to avoid buckling due to heat.
✔️ Telephone wires sag more in summer due to expansion.
✔️ Glass utensils crack when heated suddenly (thermal stress).

🟢 6. Specific Heat Capacity
It is the heat required to raise the temperature of 1 kg of a substance by 1 K.
➡️ Q = m c ΔT
where
Q = heat supplied,
m = mass,
c = specific heat capacity,
ΔT = temperature change.
💡 Unit: J·kg⁻¹·K⁻¹
✔️ Water has very high specific heat (4186 J·kg⁻¹·K⁻¹), making it ideal for temperature regulation.

🔴 7. Molar Heat Capacity
It is the heat required to raise the temperature of 1 mole of a substance by 1 K.
➡️ C = Q / (n ΔT)
where n = number of moles.
Relation: C = M c,
where M = molar mass.

🟡 8. Principle of Calorimetry
When two bodies at different temperatures are mixed, heat lost by the hotter body equals heat gained by the colder body (if no heat loss to surroundings).
➡️ m₁ c₁ (T₁ − T) = m₂ c₂ (T − T₂)
✔️ Used to determine specific heat, latent heat, etc.

🔵 9. Change of State and Latent Heat
When a substance changes its phase (solid ⇄ liquid ⇄ gas), its temperature remains constant even though heat is exchanged.
💡 Latent Heat (L):
Amount of heat required to change the state of 1 kg of substance without temperature change.
➡️ Q = m L
✔️ Latent heat of fusion: Solid → Liquid
✔️ Latent heat of vaporisation: Liquid → Gas

🟢 10. Values for Water
Latent heat of fusion (L_f) = 3.34 × 10⁵ J·kg⁻¹
Latent heat of vaporisation (L_v) = 2.26 × 10⁶ J·kg⁻¹
💧 These high values make water an excellent coolant and temperature stabiliser.

🔴 11. Modes of Heat Transfer
Heat can be transferred by conduction, convection, or radiation.

(a) Conduction
Heat transfer within a body without movement of particles.
➡️ Q = (k A ΔT t) / L
where
k = thermal conductivity,
A = cross-sectional area,
L = length,
ΔT = temperature difference,
t = time.
✔️ Metals like copper, silver are good conductors.

(b) Convection
Transfer of heat by movement of fluid particles (liquids/gases).
💡 Example: Sea and land breezes arise due to convection currents.

(c) Radiation
Transfer of heat without any medium, via electromagnetic waves.
✔️ Stefan–Boltzmann law:
➡️ E = σ T⁴,
where σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴
All bodies emit and absorb radiation; good absorbers are also good emitters.

🟡 12. Newton’s Law of Cooling
Rate of cooling ∝ temperature difference between body and surroundings.
➡️ dT/dt ∝ (T − Tₛ)
✔️ Valid for small temperature differences.
💡 Used in designing radiators and measuring emissivity.

🔵 13. Thermal Conductivity (k)
The property that quantifies how well a material conducts heat.
➡️ Rate of heat flow (Q/t) = (k A ΔT) / L
✔️ Unit: W·m⁻¹·K⁻¹
✔️ Metals → high k, good conductors
✔️ Air, wood → low k, insulators

🟢 14. Expansion of Liquids and Gases
Liquids expand more than solids; gases expand even more due to weak molecular forces.
➡️ ΔV = γ V₀ ΔT
For gases (at constant pressure),
➡️ V ∝ T (Charles’ Law)

🔴 15. Thermal Stress and Strain
If expansion is prevented, the body develops thermal stress.
➡️ Stress = Y α ΔT
where
Y = Young’s modulus,
α = coefficient of linear expansion,
ΔT = temperature change.
💡 Example: Sudden cooling of glass causes it to crack.

🟡 16. Relation Between Heat Capacities (for Gases)
For gases,
➡️ C_p − C_v = R
where
R = universal gas constant = 8.314 J·mol⁻¹·K⁻¹
✔️ Ratio γ = C_p / C_v characterises gas behaviour.

🔵 17. Calorimetry Applications
1️⃣ Mixing of Ice and Water:
m₁ c₁ (T₁ − T) = m₂ L_f + m₂ c₂ (T − 0)
2️⃣ Steam Condensation:
m_steam L_v + m_steam c_steam (100 − T) = m_water c_water (T − T₀)
💡 Principle: Heat Lost = Heat Gained

🟢 18. Real-Life Examples of Thermal Effects
✔️ Metal lids loosen on heating (expansion).
✔️ Bimetallic strips in thermostats bend with temperature change.
✔️ Sea water moderates coastal climate (high specific heat).
✔️ Ice floats due to lower density compared to water.

🔴 19. Important Constants
✔️ Specific heat of water = 4.18 × 10³ J·kg⁻¹·K⁻¹
✔️ Specific heat of ice = 2.10 × 10³ J·kg⁻¹·K⁻¹
✔️ Specific heat of steam = 2.01 × 10³ J·kg⁻¹·K⁻¹
✔️ Stefan constant σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴

🌟 SUMMARY (≈300 words)
Heat is energy transferred due to temperature difference.
Temperature measures thermal state; unit = Kelvin.
Substances expand with temperature rise:
ΔL = αL₀ΔT, ΔA = βA₀ΔT, ΔV = γV₀ΔT.
Water shows anomalous expansion: densest at 4°C.
Specific heat capacity (c): Q = m c ΔT.
Latent heat (L): Q = mL for phase change at constant temperature.
Thermal conductivity (k): rate of heat flow = (kAΔT)/L.
Heat transfer modes: conduction, convection, and radiation.
Stefan–Boltzmann law: E = σT⁴.
Newton’s cooling: dT/dt ∝ (T − Tₛ).
Stress due to restricted expansion: Stress = Y α ΔT.
For gases: C_p − C_v = R.
Calorimetry uses conservation of heat to find c or L.
Water’s high specific heat regulates climate and life processes.

🧠 QUICK RECAP
✔️ Q = m c ΔT → Heat–Temperature relation
✔️ Q = mL → Latent Heat
✔️ P = σT⁴ → Radiation law
✔️ Stress = Y α ΔT → Thermal Stress
✔️ C_p − C_v = R → Gas law
✔️ E = σT⁴, dT/dt ∝ (T − Tₛ) → Radiation & Cooling

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QUESTIONS FROM TEXTBOOK

🔵 Question 10.1
The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales.
Answer:
🟢 Step 1: Convert Kelvin to Celsius
➡️ Formula: T(°C) = T(K) − 273.15
For Neon:
T₁(°C) = 24.57 − 273.15 = −248.58 °C
For Carbon dioxide:
T₂(°C) = 216.55 − 273.15 = −56.60 °C
🟡 Step 2: Convert Celsius to Fahrenheit
➡️ Formula: T(°F) = (9/5) × T(°C) + 32
For Neon:
T₁(°F) = (9/5) × (−248.58) + 32 = −415.44 °F
For Carbon dioxide:
T₂(°F) = (9/5) × (−56.60) + 32 = −69.88 °F
✔️ Final Answers:
Neon → −248.58 °C = −415.44 °F
Carbon dioxide → −56.60 °C = −69.88 °F

🔵 Question 10.2
Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between T_A and T_B?
Answer:
🟢 Step 1: The triple point of water = 273.16 K
Therefore,
200 A = 273.16 K and 350 B = 273.16 K
🟡 Step 2: Express 1 A and 1 B in Kelvin
1 A = 273.16 / 200 = 1.3658 K
1 B = 273.16 / 350 = 0.7804 K
🟠 Step 3: Relation between T_A and T_B
T_A (in A-units) = T_B (in B-units)
T_A × 1.3658 = T_B × 0.7804
Hence,
T_B = 1.75 T_A
✔️ Final Relation: T_B = 1.75 T_A

🔵 Question 10.3
The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law
R = R₀ [1 + α(T − T₀)]
The resistance is 101.6 Ω at the triple point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?
Answer:
🟢 Given:
R₀ = 101.6 Ω, T₀ = 273.16 K
R = 165.5 Ω at T = 600.5 K
Find α and then temperature for R = 123.4 Ω
🟡 Step 1: Using the formula
165.5 = 101.6 [1 + α(600.5 − 273.16)]
Divide both sides by 101.6:
1 + α(327.34) = 165.5 / 101.6 = 1.628
α = (1.628 − 1) / 327.34 = 0.00192 K⁻¹
🟠 Step 2: For R = 123.4 Ω
123.4 = 101.6 [1 + 0.00192 (T − 273.16)]
Divide both sides by 101.6:
1 + 0.00192 (T − 273.16) = 1.215
0.00192 (T − 273.16) = 0.215
T − 273.16 = 112.0
🔴 Step 3:
T = 385.16 K
✔️ Final Answer: Temperature ≈ 385 K

🔵 Question 10.4(a)
The triple point of water is a standard fixed point in modern thermometry. Why? What is wrong in taking the melting point and boiling point of water as standard fixed points?
Answer:
✔️ The triple point of water (273.16 K) is a unique, reproducible, and precise temperature independent of pressure and impurities.
❌ The melting and boiling points of water vary with atmospheric pressure and impurities, so they cannot serve as accurate fixed points.

🔵 Question 10.4(b)
In the Celsius scale, 0 °C and 100 °C were fixed at the melting and boiling points of water. On the absolute scale (Kelvin), one fixed point is 273.16 K. What is the other fixed point?
Answer:
Each 100 °C interval corresponds to 100 K.
Hence, second fixed point = 273.16 + 100 = 373.16 K.
✔️ Other fixed point: 373.16 K

🔵 Question 10.4(c)
The absolute temperature (Kelvin scale) T and Celsius temperature t_c are related as
t_c = T − 273.15
Why do we have 273.15 and not 273.16?
Answer:
273.15 K corresponds exactly to 0 °C by international agreement for simplicity in conversion.
The true triple point (273.16 K) differs by 0.01 K, which is negligible and ignored in practical use.

🔵 Question 10.4(d)
What is the temperature of the triple point of water on an absolute scale whose unit interval equals that of the Fahrenheit scale?
Answer:
💡 The Fahrenheit scale has 180 divisions for 100 °C interval.
Therefore, 1 K = 1.8 °F.
Triple point of water = 273.16 K = 273.16 × 1.8 = 491.7 on this scale.
✔️ Final Answer: 491.7 absolute Fahrenheit units

🔵 Question 10.5
Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made:
Triple point of water:
Pressure for thermometer A = 1.250 × 10⁵ Pa
Pressure for thermometer B = 0.200 × 10⁵ Pa
Normal melting point of sulphur:
Pressure for thermometer A = 1.797 × 10⁵ Pa
Pressure for thermometer B = 0.287 × 10⁵ Pa
(a) What is the absolute temperature of normal melting point of sulphur as read by thermometers A and B?
Answer:
🟢 For thermometer A:
T₂ / T₁ = P₂ / P₁
T₁ = 273.16 K
P₂ / P₁ = 1.797 / 1.250 = 1.4376
T₂ = 273.16 × 1.4376 = 392.6 K
🟡 For thermometer B:
P₂ / P₁ = 0.287 / 0.200 = 1.435
T₂ = 273.16 × 1.435 = 392.2 K
✔️ Final Answer: 392 K (approximately for both A and B)

(b) What is the reason behind the slight difference in readings of thermometers A and B? What further step is needed?
Answer:
🔵 The small difference arises because real gases slightly deviate from ideal gas behaviour, and different gases have different compressibilities.
🟢 To minimize this difference, readings should be extrapolated to zero pressure, where gases behave ideally and all thermometers give identical results.
✔️ After extrapolation, both thermometers will agree exactly.

🔵 Question 10.6
A steel tape 1 m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10⁻⁵ K⁻¹.
Answer
🟢 Step 1: Expansion factor of the tape at 45 °C
➡️ ΔT = 45 − 27 = 18 K
➡️ Scale factor = 1 + αΔT = 1 + (1.20×10⁻⁵)(18) = 1.000216
🟡 Step 2: Convert the reading (63.0 cm) to actual length at 45 °C
➡️ L₄₅ = (0.630 m) × 1.000216 = 0.630136 m = 63.014 cm
🔴 Step 3: Find length at 27 °C (rod is also steel)
➡️ L₂₇ = L₄₅ / (1 + αΔT) = 0.630136 / 1.000216 = 0.630 m = 63.0 cm
✔️ Final: Actual length at 45 °C ≈ 63.014 cm; length at 27 °C = 63.0 cm.

🔵 Question 10.7
A large steel wheel is to be fitted on to a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? (α_steel = 1.20 × 10⁻⁵ K⁻¹.)
Answer
🟢 Step 1: Let shaft temperature be T (°C). For slipping, D_shaft(T) = D_hole(27 °C).
➡️ 8.70[1 + α(T − 27)] = 8.69
🟡 Step 2: Solve for T
➡️ 1 + α(T − 27) = 8.69/8.70 = 0.99885
➡️ α(T − 27) = −0.00115
➡️ T − 27 = −0.00115 / (1.20×10⁻⁵) ≈ −95.8 K
✔️ Final: T ≈ −68.8 °C (≈ −69 °C).

🔵 Question 10.8
A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? (α_cu = 1.70 × 10⁻⁵ K⁻¹.)
Answer
🟢 Step 1: ΔT = 227 − 27 = 200 K
🟡 Step 2: Holes expand like the material: ΔD = D α ΔT
➡️ ΔD = 4.24 × (1.70×10⁻⁵) × 200 = 0.0144 cm = 0.144 mm
✔️ Final: Increase in diameter = 0.0144 cm (new diameter ≈ 4.254 cm).

🔵 Question 10.9
A brass wire 1.8 m long at 27 °C is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of −39 °C, what is the tension developed in the wire, if its diameter is 2.0 mm? (α_brass = 2.0 × 10⁻⁵ K⁻¹; Y_brass = 0.91 × 10¹¹ Pa.)
Answer
🟢 Step 1: Temperature fall
➡️ ΔT = (−39 − 27) = −66 K (magnitude 66 K)
🟡 Step 2: Thermal strain prevented ⇒ stress = Y α ΔT
➡️ σ = (0.91×10¹¹)(2.0×10⁻⁵)(66) = 1.20×10⁸ Pa
🟠 Step 3: Cross-sectional area (d = 2.0 mm = 2.0×10⁻³ m)
➡️ A = (π/4)d² = π×10⁻⁶ m²
🔴 Step 4: Tension
➡️ F = σA = (1.20×10⁸)(π×10⁻⁶) ≈ 3.77×10² N
✔️ Final: Tension ≈ 3.8 × 10² N (≈ 377 N).

🔵 Question 10.10
A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250 °C, if the original lengths are at 40.0 °C? Is there a ‘thermal stress’ developed at the junction? (α_brass = 2.0 × 10⁻⁵ K⁻¹, α_steel = 1.2 × 10⁻⁵ K⁻¹.) Ends are free to expand.
Answer
🟢 Step 1: ΔT = 250 − 40 = 210 K; L₀ (each) = 0.50 m
🟡 Step 2: Individual expansions
➡️ Brass: ΔL_b = L₀ α_b ΔT = 0.50×(2.0×10⁻⁵)×210 = 0.00210 m = 2.10 mm
➡️ Steel: ΔL_s = L₀ α_s ΔT = 0.50×(1.2×10⁻⁵)×210 = 0.00126 m = 1.26 mm
🟠 Step 3: Net expansion of combination
➡️ ΔL_total = ΔL_b + ΔL_s = 3.36 mm
🔴 Stress check (free ends): No external constraint ⇒ no thermal stress at the junction.
✔️ Final: Total expansion = 3.36 mm; no thermal stress develops.

🔵 Question 10.11
The coefficient of volume expansion of glycerine is 49 × 10⁻⁵ K⁻¹. What is the fractional change in its density for a 30 °C rise in temperature?
Answer
🟢 Step 1: For small changes, ρ ∝ 1/V ⇒ (Δρ/ρ) ≈ −βΔT
➡️ β = 49×10⁻⁵ = 4.9×10⁻⁴ K⁻¹
🟡 Step 2: Compute
➡️ Δρ/ρ = −(4.9×10⁻⁴)(30) = −1.47×10⁻²
✔️ Final: Fractional change in density = −0.0147 (i.e., density decreases by 1.47%).

🔵 Question 10.12
A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used in heating the machine itself or lost to the surroundings? (Specific heat of aluminium = 0.91 J g⁻¹ K⁻¹.)
Answer
🟢 Step 1: Effective power to block
➡️ P_eff = 0.5 × 10 kW = 5 kW = 5000 J s⁻¹
🟡 Step 2: Heat supplied in t = 2.5 min = 150 s
➡️ Q = P_eff × t = 5000 × 150 = 7.5×10⁵ J
🟠 Step 3: Use Q = m c ΔT with c_Al = 0.91 J g⁻¹ K⁻¹ = 910 J kg⁻¹ K⁻¹
➡️ ΔT = Q/(m c) = (7.5×10⁵)/(8.0×910) ≈ 103 K
✔️ Final: Rise in temperature ≈ 1.0×10² K (about 103 °C).

🔵 Question 10.13
A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and then placed on a large ice block. What is the maximum amount of ice that can melt? (Specific heat of copper = 0.39 J g⁻¹ K⁻¹; latent heat of fusion of water = 335 J g⁻¹.)
Answer
🟢 Step 1: Heat released by copper on cooling from 500 °C to 0 °C
➡️ c_Cu = 0.39 J g⁻¹ K⁻¹ = 390 J kg⁻¹ K⁻¹
➡️ Q = m c ΔT = 2.5 × 390 × 500 = 4.875×10⁵ J
🟡 Step 2: Ice melted (L = 335 J g⁻¹ = 3.35×10⁵ J kg⁻¹)
➡️ m_ice = Q/L = (4.875×10⁵)/(3.35×10⁵) ≈ 1.46 kg
✔️ Final: Maximum ice melted ≈ 1.46 kg.

🔵 Question 10.14
In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at 150 °C is dropped into a copper calorimeter of mass 0.025 kg containing 150 cm³ of water at 27 °C. The final temperature is 40 °C. Compute the specific heat of the metal. (Neglect heat loss. Take c_water = 4.2×10³ J kg⁻¹ K⁻¹, c_copper = 0.39 J g⁻¹ K⁻¹.)
Answer
🟢 Step 1: Known data
➡️ m_m = 0.20 kg, T_m: 150 → 40 °C (ΔT_m = 110 K)
➡️ m_w = 150 cm³ = 0.150 kg, ΔT_w = 13 K
➡️ m_cu = 0.025 kg, ΔT_cu = 13 K
➡️ c_w = 4200 J kg⁻¹ K⁻¹, c_cu = 390 J kg⁻¹ K⁻¹
🟡 Step 2: Heat lost by metal = Heat gained by water + calorimeter
➡️ m_m c_m ΔT_m = m_w c_w ΔT_w + m_cu c_cu ΔT_cu
➡️ 0.20 c_m (110) = 0.150(4200)(13) + 0.025(390)(13)
🟠 Step 3: Evaluate RHS
➡️ RHS = 8190 + 126.75 = 8316.75 J
🔴 Step 4: Solve for c_m
➡️ 22 c_m = 8316.75 ⇒ c_m ≈ 378.9 J kg⁻¹ K⁻¹
✔️ Final: Specific heat of the metal ≈ 3.79 × 10² J kg⁻¹ K⁻¹ (≈ 0.38 J g⁻¹ K⁻¹).

🔵 Question 10.15
Given below are observations on molar specific heats at room temperature of some common gases:
Hydrogen → 4.87 cal mol⁻¹ K⁻¹
Nitrogen → 4.97 cal mol⁻¹ K⁻¹
Oxygen → 5.02 cal mol⁻¹ K⁻¹
Nitric oxide → 4.99 cal mol⁻¹ K⁻¹
Carbon monoxide → 5.01 cal mol⁻¹ K⁻¹
Chlorine → 6.17 cal mol⁻¹ K⁻¹
The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically, molar specific heat of a monatomic gas is 2.92 cal mol⁻¹ K⁻¹. Explain this difference. What can you infer from the somewhat larger value for chlorine?

Answer:
🟢 Step 1: Recall molar heat for monatomic gases
➡️ For a monatomic gas, only translational motion contributes to energy.
➡️ Hence, Cᵥ = (3/2)R = 2.98 cal mol⁻¹ K⁻¹ ≈ 2.92 cal mol⁻¹ K⁻¹.
🟡 Step 2: Explanation for diatomic and polyatomic gases
➡️ Diatomic gases such as H₂, N₂, O₂, NO, CO have additional rotational degrees of freedom, increasing internal energy.
➡️ Thus, Cᵥ = (5/2)R ≈ 4.97 cal mol⁻¹ K⁻¹.
✅ This matches well with the given measured values (around 4.9–5.0).
🟠 Step 3: Reason for the higher value of chlorine (6.17 cal mol⁻¹ K⁻¹)
➡️ Heavier molecules like Cl₂ have vibrational modes that begin to get excited even at room temperature.
➡️ These extra degrees of freedom absorb additional energy, slightly increasing specific heat capacity.
🔴 Step 4: Final inference
✔️ Monatomic gases → translational energy only → ~2.92 cal mol⁻¹ K⁻¹.
✔️ Diatomic gases → translational + rotational → ~5 cal mol⁻¹ K⁻¹.
✔️ Heavier diatomic gases (e.g., Cl₂) → translational + rotational + partial vibrational → ~6 cal mol⁻¹ K⁻¹.

✅ Final Answer:
The higher specific heats of diatomic gases arise from rotational energy. Chlorine’s somewhat larger value indicates the beginning of vibrational motion participation at room temperature.

🔵 Question 10.16
A child running a temperature of 101 °F is given an antipyretic medicine that causes an increase in the rate of evaporation of sweat. If the fever is brought down to 98 °F in 20 minutes, what is the average rate of extra evaporation?
Mass of child = 30 kg, specific heat of human body = that of water, latent heat of vaporization = 580 cal g⁻¹.
Answer:
🟢 Step 1: Convert to Celsius
➡️ 101 °F = (5/9)(101 − 32) = 38.3 °C
➡️ 98 °F = (5/9)(98 − 32) = 36.7 °C
➡️ ΔT = 1.6 °C
🟡 Step 2: Heat lost by body
➡️ Q = m c ΔT
➡️ m = 30 kg = 3.0×10⁴ g, c = 1 cal g⁻¹ °C⁻¹
➡️ Q = 3.0×10⁴ × 1 × 1.6 = 4.8×10⁴ cal
🟠 Step 3: Evaporation of sweat (latent heat = 580 cal g⁻¹)
➡️ m_evap = Q / L = (4.8×10⁴) / 580 ≈ 82.8 g
🔴 Step 4: Time = 20 min = 1200 s
➡️ Rate = 82.8 g / 1200 s = 0.069 g s⁻¹
✔️ Final Answer: Average rate of extra evaporation = 0.069 g s⁻¹ (≈ 70 mg/s).

🔵 Question 10.17
A ‘thermocol’ icebox (30 cm cube, wall thickness 5 cm, k = 0.01 J s⁻¹ m⁻¹ K⁻¹) is used for storing cooked food. If 4.0 kg of ice is put in the box, estimate the amount of ice remaining after 6 h when the outside temperature is 45 °C.
Latent heat of fusion of water = 3.35×10⁵ J kg⁻¹.
Answer:
🟢 Step 1: Dimensions
Outer side = 30 cm = 0.30 m → inner side = 0.20 m (subtract twice the thickness).
Area for heat transfer ≈ 6 × (0.20)² = 0.24 m²
🟡 Step 2: Heat flow rate
➡️ Q̇ = kAΔT / x
➡️ Q̇ = (0.01)(0.24)(45 − 0)/0.05 = 2.16 J s⁻¹
🟠 Step 3: Total heat in 6 h
➡️ t = 6×3600 = 21600 s
➡️ Q = 2.16 × 21600 = 4.67×10⁴ J
🔴 Step 4: Ice melted
➡️ m = Q / L = (4.67×10⁴)/(3.35×10⁵) = 0.139 kg
✔️ Final Answer: Ice melted = 0.14 kg,
Ice remaining = 4.00 − 0.14 = 3.86 kg.

🔵 Question 10.18
A brass boiler has a base area 0.15 m² and thickness 1.0 cm. It boils water at the rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler.
Thermal conductivity of brass = 109 J s⁻¹ m⁻¹ K⁻¹, heat of vaporization of water = 2.26×10⁶ J kg⁻¹.
Answer:
🟢 Step 1: Heat conducted through brass = heat used for vaporization
➡️ Q/t = kAΔT / x = mL / t
🟡 Step 2: Substitute
m = 6 kg/min = 0.1 kg/s, L = 2.26×10⁶ J/kg, A = 0.15 m², x = 0.01 m, k = 109
➡️ (0.1)(2.26×10⁶) = 109×0.15×(ΔT)/0.01
➡️ 2.26×10⁵ = 1635 ΔT
➡️ ΔT = 138 K
🟠 Step 3: Water boiling temperature = 100 °C → flame side T = 100 + 138 = 238 °C
✔️ Final Answer: Temperature at contact with flame = 238 °C.

🔵 Question 10.19
Explain why:
(a) A body with large reflectivity is a poor emitter.
➡️ High reflectivity means less absorption; by Kirchhoff’s law, good absorbers are good emitters. Hence, a highly reflective surface emits poorly.
(b) A brass tumbler feels much colder than a wooden tray on a chilly day.
➡️ Brass is a better conductor; it draws heat rapidly from your hand, making it feel colder.
(c) An optical pyrometer calibrated for an ideal black body gives low readings for real objects.
➡️ Real bodies emit less radiation than a black body; hence apparent temperature is lower.
(d) The earth would be inhospitably cold without its atmosphere.
➡️ Greenhouse gases absorb and re-radiate infrared heat, maintaining warmth. Without this, heat would escape rapidly into space.
(e) Houses with whitewashed walls are cooler in summer.
➡️ White surfaces reflect sunlight, absorbing less heat, keeping interiors cooler.
✔️ Concept: Reflectivity and emissivity are complementary; conduction and radiation govern thermal sensations.

🔵 Question 10.20
A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of surroundings is 20 °C.
Answer:
🟢 Step 1: Use Newton’s law of cooling
➡️ Rate ∝ (T − T_s), ⇒ (T − T_s)/(T₀ − T_s) = e^(−kt)
🟡 Step 2: From first data
For 80 → 50 °C in 5 min (300 s), T_s = 20 °C
(50 − 20)/(80 − 20) = e^(−k×300)
➡️ 30/60 = 0.5 = e^(−300k)
➡️ k = (ln 2)/300 = 0.00231 s⁻¹
🟠 Step 3: For 60 → 30 °C,
(30 − 20)/(60 − 20) = e^(−k t)
➡️ 10/40 = 0.25 = e^(−0.00231t)
➡️ ln(0.25) = −0.00231t
➡️ t = (1.3863)/0.00231 = 600 s
✔️ Final Answer: Time to cool = 10 minutes.

NEET QUESTIONS FROM THIS LESSON

🔴 Question 1 (NEET 2024):
When water is heated from 0°C to 10°C, its volume
🟢 1️⃣ First decreases and then increases
🟡 2️⃣ Increases steadily
🔵 3️⃣ Decreases steadily
🟣 4️⃣ Remains constant
✅ Answer: 1️⃣ First decreases and then increases

🔴 Question 2 (NEET 2023):
The coefficient of linear expansion of a rod is α. The fractional change in its length when temperature increases by T is
🟢 1️⃣ αT
🟡 2️⃣ 2αT
🔵 3️⃣ α/T
🟣 4️⃣ T/α
✅ Answer: 1️⃣ αT

🔴 Question 3 (NEET 2022):
At 4°C, the density of water is maximum because
🟢 1️⃣ The decrease due to increase in temperature is compensated by anomalous expansion
🟡 2️⃣ Hydrogen bonding is strongest
🔵 3️⃣ Water molecules are closest
🟣 4️⃣ Ice melts at 4°C
✅ Answer: 3️⃣ Water molecules are closest

🔴 Question 4 (NEET 2021):
Which one of the following is not a unit of heat?
🟢 1️⃣ Calorie
🟡 2️⃣ Joule
🔵 3️⃣ Erg
🟣 4️⃣ Watt
✅ Answer: 4️⃣ Watt

🔴 Question 5 (NEET 2020):
Two rods of same length and material but different cross-sections are heated equally. Which statement is true?
🟢 1️⃣ Both expand equally in length
🟡 2️⃣ Thicker rod expands more
🔵 3️⃣ Thinner rod expands more
🟣 4️⃣ No expansion occurs
✅ Answer: 1️⃣ Both expand equally in length

🔴 Question 6 (NEET 2019):
Which of the following statements is true for a perfectly black body?
🟢 1️⃣ Absorbs all radiations
🟡 2️⃣ Reflects all radiations
🔵 3️⃣ Transmits all radiations
🟣 4️⃣ Absorbs and reflects equally
✅ Answer: 1️⃣ Absorbs all radiations

🔴 Question 7 (NEET 2018):
Stefan–Boltzmann law states that
🟢 1️⃣ E ∝ T⁴
🟡 2️⃣ E ∝ T
🔵 3️⃣ E ∝ 1/T
🟣 4️⃣ E ∝ T²
✅ Answer: 1️⃣ E ∝ T⁴

🔴 Question 8 (NEET 2017):
Emissivity of a perfect black body is
🟢 1️⃣ 0
🟡 2️⃣ 1
🔵 3️⃣ 0.5
🟣 4️⃣ Infinity
✅ Answer: 2️⃣ 1

🔴 Question 9 (NEET 2016):
The ratio of emissive power to absorptive power for a body is
🟢 1️⃣ Constant
🟡 2️⃣ Equal to emissivity
🔵 3️⃣ Equal to absorptivity
🟣 4️⃣ Equal to Stefan constant
✅ Answer: 1️⃣ Constant

🔴 Question 10 (AIPMT 2015):
The unit of Stefan’s constant is
🟢 1️⃣ W m⁻² K⁻⁴
🟡 2️⃣ J m⁻² K⁻¹
🔵 3️⃣ W m⁻²
🟣 4️⃣ J K⁻¹
✅ Answer: 1️⃣ W m⁻² K⁻⁴

🔴 Question 11 (AIPMT 2014):
Which of the following is a good conductor of heat?
🟢 1️⃣ Silver
🟡 2️⃣ Wood
🔵 3️⃣ Glass
🟣 4️⃣ Plastic
✅ Answer: 1️⃣ Silver

🔴 Question 12 (AIPMT 2013):
In a calorimeter, when a hot solid is mixed with cold water, the temperature becomes constant due to
🟢 1️⃣ Thermal equilibrium
🟡 2️⃣ Loss of heat only
🔵 3️⃣ Gain of heat only
🟣 4️⃣ Radiation
✅ Answer: 1️⃣ Thermal equilibrium

🔴 Question 13 (AIPMT 2012):
When temperature increases, surface tension
🟢 1️⃣ Decreases
🟡 2️⃣ Increases
🔵 3️⃣ Remains same
🟣 4️⃣ First increases then decreases
✅ Answer: 1️⃣ Decreases

🔴 Question 14 (AIPMT 2011):
Latent heat is associated with
🟢 1️⃣ Change in temperature
🟡 2️⃣ Change in phase
🔵 3️⃣ Change in pressure
🟣 4️⃣ Change in volume
✅ Answer: 2️⃣ Change in phase

🔴 Question 15 (AIPMT 2010):
At 0°C, the density of water is
🟢 1️⃣ 1.000 g/cm³
🟡 2️⃣ 0.998 g/cm³
🔵 3️⃣ 1.1 g/cm³
🟣 4️⃣ 0.95 g/cm³
✅ Answer: 2️⃣ 0.998 g/cm³

🔴 Question 16 (AIPMT 2009):
Thermal conductivity of metals is due to
🟢 1️⃣ Free electrons
🟡 2️⃣ Lattice vibrations
🔵 3️⃣ Phonons
🟣 4️⃣ Convection
✅ Answer: 1️⃣ Free electrons

🔴 Question 17 (AIPMT 2008):
Which of the following has the least thermal conductivity?
🟢 1️⃣ Air
🟡 2️⃣ Water
🔵 3️⃣ Glass
🟣 4️⃣ Silver
✅ Answer: 1️⃣ Air

🔴 Question 18 (AIPMT 2007):
Newton’s law of cooling is valid when
🟢 1️⃣ Temperature difference is small
🟡 2️⃣ Temperature difference is large
🔵 3️⃣ Medium is vacuum
🟣 4️⃣ Radiation is negligible
✅ Answer: 1️⃣ Temperature difference is small

🔴 Question 19 (AIPMT 2006):
In an adiabatic process
🟢 1️⃣ No exchange of heat
🟡 2️⃣ No work done
🔵 3️⃣ Temperature constant
🟣 4️⃣ Pressure constant
✅ Answer: 1️⃣ No exchange of heat

🔴 Question 20 (AIPMT 2005):
Good absorbers are
🟢 1️⃣ Good emitters
🟡 2️⃣ Poor emitters
🔵 3️⃣ Good reflectors
🟣 4️⃣ Poor reflectors
✅ Answer: 1️⃣ Good emitters

🔴 Question 21 (AIPMT 2004):
Thermal expansion is minimum in
🟢 1️⃣ Solids
🟡 2️⃣ Liquids
🔵 3️⃣ Gases
🟣 4️⃣ Equal in all
✅ Answer: 1️⃣ Solids

🔴 Question 22 (AIPMT 2003):
The specific heat of water is maximum at
🟢 1️⃣ 0°C
🟡 2️⃣ 4°C
🔵 3️⃣ 100°C
🟣 4️⃣ −4°C
✅ Answer: 2️⃣ 4°C

🔴 Question 23 (AIPMT 2002):
Anomalous expansion of water is maximum at
🟢 1️⃣ 4°C
🟡 2️⃣ 0°C
🔵 3️⃣ 100°C
🟣 4️⃣ 273°C
✅ Answer: 1️⃣ 4°C

🔴 Question 24 (AIPMT 2001):
Unit of thermal conductivity in SI is
🟢 1️⃣ W m⁻¹ K⁻¹
🟡 2️⃣ J m⁻¹ K⁻¹
🔵 3️⃣ cal cm⁻¹ s⁻¹ °C⁻¹
🟣 4️⃣ erg cm⁻¹ s⁻¹ °C⁻¹
✅ Answer: 1️⃣ W m⁻¹ K⁻¹

🔴 Question 25 (NEET 2024):
A metallic rod expands 0.2% in length when heated by 100°C. Its coefficient of linear expansion is
🟢 1️⃣ 2 × 10⁻⁵ °C⁻¹
🟡 2️⃣ 4 × 10⁻⁵ °C⁻¹
🔵 3️⃣ 2 × 10⁻⁶ °C⁻¹
🟣 4️⃣ 4 × 10⁻⁶ °C⁻¹
✅ Answer: 1️⃣ 2 × 10⁻⁵ °C⁻¹

🔴 Question 26 (NEET 2023):
Two spheres of same material have radii r₁ and r₂. The ratio of their heat radiation at same temperature is
🟢 1️⃣ r₁² : r₂²
🟡 2️⃣ r₁³ : r₂³
🔵 3️⃣ r₁ : r₂
🟣 4️⃣ 1 : 1
✅ Answer: 1️⃣ r₁² : r₂²

🔴 Question 27 (NEET 2022):
A metal rod of length L is heated. Its length increases by ΔL. The linear expansion coefficient is
🟢 1️⃣ ΔL / (L × ΔT)
🟡 2️⃣ L / (ΔL × ΔT)
🔵 3️⃣ ΔT / (L × ΔL)
🟣 4️⃣ ΔL × L / ΔT
✅ Answer: 1️⃣ ΔL / (L × ΔT)

🔴 Question 28 (NEET 2021):
A black body radiates energy at the rate of E at 127°C. At 227°C, rate will be
🟢 1️⃣ 2E
🟡 2️⃣ 4E
🔵 3️⃣ 16E
🟣 4️⃣ 8E
✅ Answer: 3️⃣ 16E

🔴 Question 29 (NEET 2020):
The emissive power is directly proportional to
🟢 1️⃣ T⁴
🟡 2️⃣ T³
🔵 3️⃣ T²
🟣 4️⃣ T
✅ Answer: 1️⃣ T⁴

🔴 Question 30 (NEET 2019):
A calorimeter of mass 100 g contains 200 g of water. 50 g steam at 100°C is passed. Final temperature is
🟢 1️⃣ 100°C
🟡 2️⃣ 90°C
🔵 3️⃣ 80°C
🟣 4️⃣ 60°C
✅ Answer: 1️⃣ 100°C

🔴 Question 31 (NEET 2018):
In steady state, heat conducted per second through a rod depends on
🟢 1️⃣ Area and temperature difference
🟡 2️⃣ Area, temperature difference, length
🔵 3️⃣ Only length
🟣 4️⃣ Only temperature
✅ Answer: 2️⃣ Area, temperature difference, length

🔴 Question 32 (NEET 2017):
The relation between coefficient of volume and linear expansion is
🟢 1️⃣ β = 3α
🟡 2️⃣ β = α
🔵 3️⃣ β = 2α
🟣 4️⃣ β = α/3
✅ Answer: 1️⃣ β = 3α

🔴 Question 33 (NEET 2016):
Newton’s law of cooling states that
🟢 1️⃣ Rate of cooling ∝ temperature difference
🟡 2️⃣ Rate of cooling ∝ square of temperature difference
🔵 3️⃣ Rate of cooling ∝ cube of temperature difference
🟣 4️⃣ Rate of cooling ∝ reciprocal of temperature
✅ Answer: 1️⃣ Rate of cooling ∝ temperature difference

🔴 Question 34 (AIPMT 2015):
Which mode of heat transfer does not require medium?
🟢 1️⃣ Radiation
🟡 2️⃣ Conduction
🔵 3️⃣ Convection
🟣 4️⃣ All need medium
✅ Answer: 1️⃣ Radiation

🔴 Question 35 (AIPMT 2014):
Stefan’s constant σ has units
🟢 1️⃣ W m⁻² K⁻⁴
🟡 2️⃣ J m⁻² K⁻¹
🔵 3️⃣ W m⁻² K⁻¹
🟣 4️⃣ J m⁻²
✅ Answer: 1️⃣ W m⁻² K⁻⁴

🔴 Question 36 (AIPMT 2013):
If 1 cal = 4.2 J, then specific heat 0.5 cal/g°C =
🟢 1️⃣ 2.1 J/g°C
🟡 2️⃣ 4.2 J/g°C
🔵 3️⃣ 8.4 J/g°C
🟣 4️⃣ 1.05 J/g°C
✅ Answer: 1️⃣ 2.1 J/g°C

🔴 Question 37 (AIPMT 2012):
The relation between Cₚ and Cᵥ is
🟢 1️⃣ Cₚ − Cᵥ = R
🟡 2️⃣ Cₚ = Cᵥ
🔵 3️⃣ Cₚ = R Cᵥ
🟣 4️⃣ Cᵥ − Cₚ = R
✅ Answer: 1️⃣ Cₚ − Cᵥ = R

🔴 Question 38 (AIPMT 2011):
A 1 m rod expands 1 mm on heating by 100°C. Its α is
🟢 1️⃣ 10⁻⁵ /°C
🟡 2️⃣ 10⁻⁶ /°C
🔵 3️⃣ 10⁻⁴ /°C
🟣 4️⃣ 10⁻³ /°C
✅ Answer: 1️⃣ 10⁻⁵ /°C

🔴 Question 39 (AIPMT 2010):
The heat required to raise 1 g of water by 1°C is
🟢 1️⃣ 1 cal
🟡 2️⃣ 4.2 J
🔵 3️⃣ Both 1 cal and 4.2 J
🟣 4️⃣ 0.5 cal
✅ Answer: 3️⃣ Both 1 cal and 4.2 J

🔴 Question 40 (AIPMT 2009):
In thermal conduction, steady state means
🟢 1️⃣ Temperature of each section constant
🟡 2️⃣ No heat flow
🔵 3️⃣ Heat flow zero
🟣 4️⃣ Temperature rises continuously
✅ Answer: 1️⃣ Temperature of each section constant

🔴 Question 41 (AIPMT 2008):
When temperature increases, viscosity of liquid
🟢 1️⃣ Decreases
🟡 2️⃣ Increases
🔵 3️⃣ Remains constant
🟣 4️⃣ First decreases then increases
✅ Answer: 1️⃣ Decreases

🔴 Question 42 (AIPMT 2007):
Radiation energy absorbed by black body is
🟢 1️⃣ Maximum
🟡 2️⃣ Minimum
🔵 3️⃣ Zero
🟣 4️⃣ Infinite
✅ Answer: 1️⃣ Maximum

🔴 Question 43 (AIPMT 2006):
At thermal equilibrium, emissivity =
🟢 1️⃣ Absorptivity
🟡 2️⃣ Reflectivity
🔵 3️⃣ 1 − Absorptivity
🟣 4️⃣ None
✅ Answer: 1️⃣ Absorptivity

🔴 Question 44 (AIPMT 2005):
Which has maximum specific heat?
🟢 1️⃣ Water
🟡 2️⃣ Iron
🔵 3️⃣ Silver
🟣 4️⃣ Copper
✅ Answer: 1️⃣ Water

🔴 Question 45 (AIPMT 2004):
Radiation from a body depends on
🟢 1️⃣ Temperature
🟡 2️⃣ Nature of surface
🔵 3️⃣ Area
🟣 4️⃣ All of these
✅ Answer: 4️⃣ All of these

🔴 Question 46 (AIPMT 2003):
A perfect black body
🟢 1️⃣ Absorbs all
🟡 2️⃣ Reflects all
🔵 3️⃣ Transmits all
🟣 4️⃣ None
✅ Answer: 1️⃣ Absorbs all

🔴 Question 47 (AIPMT 2002):
Good reflectors are
🟢 1️⃣ Poor absorbers
🟡 2️⃣ Good absorbers
🔵 3️⃣ Good radiators
🟣 4️⃣ Good conductors
✅ Answer: 1️⃣ Poor absorbers

🔴 Question 48 (AIPMT 2001):
If temperature difference doubles, rate of conduction becomes
🟢 1️⃣ Doubled
🟡 2️⃣ Halved
🔵 3️⃣ Same
🟣 4️⃣ Quadrupled
✅ Answer: 1️⃣ Doubled

🔴 Question 49 (NEET 2024):
If area doubles, length same, temperature difference same, conduction rate
🟢 1️⃣ Doubles
🟡 2️⃣ Halves
🔵 3️⃣ Remains same
🟣 4️⃣ Becomes zero
✅ Answer: 1️⃣ Doubles

🔴 Question 50 (NEET 2025):
According to Stefan–Boltzmann law, radiation power is proportional to
🟢 1️⃣ T⁴
🟡 2️⃣ T³
🔵 3️⃣ T²
🟣 4️⃣ T
✅ Answer: 1️⃣ T⁴

JEE MAINS QUESTIONS FROM THIS LESSON

🔴 Q1. The coefficient of linear expansion (α) of a material is related to the coefficient of volumetric expansion (γ) as
🟢 1️⃣ γ = 3α
🔵 2️⃣ γ = α
🟡 3️⃣ γ = 2α
🟣 4️⃣ γ = α/3
✔️ Answer: 1
📘 Exam: JEE Main 2024

🔴 Q2. When temperature increases, the time period of a simple pendulum
🟢 1️⃣ Increases
🔵 2️⃣ Decreases
🟡 3️⃣ Remains same
🟣 4️⃣ Becomes zero
✔️ Answer: 1
📘 Exam: JEE Main 2023

🔴 Q3. The unit of coefficient of thermal conductivity is
🟢 1️⃣ W m⁻¹ K⁻¹
🔵 2️⃣ J K⁻¹
🟡 3️⃣ W K⁻¹
🟣 4️⃣ J m⁻¹ s⁻¹
✔️ Answer: 1
📘 Exam: JEE Main 2023

🔴 Q4. Two rods of same length and area but different materials are joined in series. The equivalent thermal conductivity is
🟢 1️⃣ 2k₁k₂ / (k₁ + k₂)
🔵 2️⃣ k₁ + k₂
🟡 3️⃣ √(k₁k₂)
🟣 4️⃣ (k₁k₂)/(k₁ + k₂)
✔️ Answer: 1
📘 Exam: JEE Main 2022

🔴 Q5. Thermal conductivity of a good conductor is
🟢 1️⃣ High
🔵 2️⃣ Low
🟡 3️⃣ Zero
🟣 4️⃣ Depends on length
✔️ Answer: 1
📘 Exam: JEE Main 2022

🔴 Q6. The temperature at which Celsius and Fahrenheit scales are equal is
🟢 1️⃣ −40°
🔵 2️⃣ 0°
🟡 3️⃣ 100°
🟣 4️⃣ −273°
✔️ Answer: 1
📘 Exam: JEE Main 2021

🔴 Q7. When a solid is heated, its length increases by 1%. Its area increases by approximately
🟢 1️⃣ 2%
🔵 2️⃣ 3%
🟡 3️⃣ 1%
🟣 4️⃣ 4%
✔️ Answer: 1
📘 Exam: JEE Main 2021

🔴 Q8. The ratio of thermal conductivities of copper and air is approximately
🟢 1️⃣ 10⁴
🔵 2️⃣ 10
🟡 3️⃣ 10²
🟣 4️⃣ 10³
✔️ Answer: 1
📘 Exam: JEE Main 2020

🔴 Q9. In steady state, heat conducted per second is proportional to
🟢 1️⃣ Temperature difference
🔵 2️⃣ Square of temperature difference
🟡 3️⃣ Inverse of temperature difference
🟣 4️⃣ Cube of temperature difference
✔️ Answer: 1
📘 Exam: JEE Main 2020

🔴 Q10. The specific heat of water is maximum at
🟢 1️⃣ 4°C
🔵 2️⃣ 0°C
🟡 3️⃣ 10°C
🟣 4️⃣ 100°C
✔️ Answer: 1
📘 Exam: JEE Main 2019

🔴 Q11. The amount of heat required to change the unit mass from solid to liquid is
🟢 1️⃣ Latent heat of fusion
🔵 2️⃣ Latent heat of vaporization
🟡 3️⃣ Specific heat
🟣 4️⃣ None
✔️ Answer: 1
📘 Exam: JEE Main 2019

🔴 Q12. The heat transfer that doesn’t require a medium is
🟢 1️⃣ Radiation
🔵 2️⃣ Conduction
🟡 3️⃣ Convection
🟣 4️⃣ All of these
✔️ Answer: 1
📘 Exam: JEE Main 2018

🔴 Q13. Thermal expansion occurs because
🟢 1️⃣ Intermolecular distance increases
🔵 2️⃣ Temperature decreases
🟡 3️⃣ Mass increases
🟣 4️⃣ Pressure decreases
✔️ Answer: 1
📘 Exam: JEE Main 2018

🔴 Q14. The emissivity of a perfect black body is
🟢 1️⃣ 1
🔵 2️⃣ 0
🟡 3️⃣ ∞
🟣 4️⃣ 0.5
✔️ Answer: 1
📘 Exam: JEE Main 2017

🔴 Q15. For a black body, energy radiated per unit area ∝
🟢 1️⃣ T⁴
🔵 2️⃣ T³
🟡 3️⃣ T²
🟣 4️⃣ T
✔️ Answer: 1
📘 Exam: JEE Main 2017

🔴 Q16. The dimension of Stefan’s constant is
🟢 1️⃣ [M¹T⁻³K⁻⁴]
🔵 2️⃣ [M¹L⁻¹T⁻³]
🟡 3️⃣ [M¹L¹T⁻²]
🟣 4️⃣ [M⁰L⁰T⁰]
✔️ Answer: 1
📘 Exam: JEE Main 2016

🔴 Q17. For conduction, which is correct?
🟢 1️⃣ Medium is required
🔵 2️⃣ Medium not required
🟡 3️⃣ Both possible
🟣 4️⃣ None
✔️ Answer: 1
📘 Exam: JEE Main 2016

🔴 Q18. The ratio of emissive powers of two bodies at same temperature equals the ratio of
🟢 1️⃣ Their absorptivities
🔵 2️⃣ Their reflectivities
🟡 3️⃣ Their conductivities
🟣 4️⃣ Their densities
✔️ Answer: 1
📘 Exam: JEE Main 2015

🔴 Q19. At thermal equilibrium, emissivity =
🟢 1️⃣ Absorptivity
🔵 2️⃣ 1 − Reflectivity
🟡 3️⃣ Conductivity
🟣 4️⃣ Specific heat
✔️ Answer: 1
📘 Exam: JEE Main 2015

🔴 Q20. Good absorbers are
🟢 1️⃣ Good emitters
🔵 2️⃣ Bad emitters
🟡 3️⃣ Neither
🟣 4️⃣ Perfect reflectors
✔️ Answer: 1
📘 Exam: JEE Main 2014

🔴 Q21. In which process heat transfer is maximum?
🟢 1️⃣ Radiation
🔵 2️⃣ Convection
🟡 3️⃣ Conduction
🟣 4️⃣ All equal
✔️ Answer: 1
📘 Exam: JEE Main 2014

🔴 Q22. Temperature of Sun can be found using
🟢 1️⃣ Stefan’s law
🔵 2️⃣ Boyle’s law
🟡 3️⃣ Avogadro’s law
🟣 4️⃣ Newton’s law
✔️ Answer: 1
📘 Exam: JEE Main 2013

🔴 Q23. A black body absorbs
🟢 1️⃣ All radiation
🔵 2️⃣ Only visible
🟡 3️⃣ Only IR
🟣 4️⃣ None
✔️ Answer: 1
📘 Exam: JEE Main 2013

🔴 Q24. Thermal radiation can propagate through
🟢 1️⃣ Vacuum
🔵 2️⃣ Air
🟡 3️⃣ Glass
🟣 4️⃣ All
✔️ Answer: 1
📘 Exam: JEE Main 2012

🔴 Q25. If the temperature is doubled, energy radiated increases by
🟢 1️⃣ 16 times
🔵 2️⃣ 2 times
🟡 3️⃣ 4 times
🟣 4️⃣ 8 times
✔️ Answer: 1
📘 Exam: JEE Main 2012

🔴 Q26. If emissive power is E and absorptivity is a, then power absorbed =
🟢 1️⃣ aE
🔵 2️⃣ E/a
🟡 3️⃣ a/E
🟣 4️⃣ a + E
✔️ Answer: 1
📘 Exam: JEE Main 2011

🔴 Q27. In steady state, temperature of two ends of a rod are T₁ and T₂. The temperature variation along its length is
🟢 1️⃣ Linear
🔵 2️⃣ Parabolic
🟡 3️⃣ Exponential
🟣 4️⃣ Logarithmic
✔️ Answer: 1
📘 Exam: JEE Main 2011

🔴 Q28. When temperature increases, coefficient of linear expansion
🟢 1️⃣ Remains constant
🔵 2️⃣ Decreases
🟡 3️⃣ Increases
🟣 4️⃣ Becomes zero
✔️ Answer: 1
📘 Exam: JEE Main 2010

🔴 Q29. The ratio of coefficients of area and linear expansion is
🟢 1️⃣ 2:1
🔵 2️⃣ 1:2
🟡 3️⃣ 3:1
🟣 4️⃣ 1:3
✔️ Answer: 1
📘 Exam: JEE Main 2010

🔴 Q30. The relation between Celsius and Fahrenheit is
🟢 1️⃣ F = (9/5)C + 32
🔵 2️⃣ F = (5/9)C + 32
🟡 3️⃣ F = (9/5)(C – 32)
🟣 4️⃣ F = C + 32
✔️ Answer: 1
📘 Exam: JEE Main 2009

🔴 Q31. In a thermally insulated container, two liquids at different temperatures are mixed. The final temperature is
🟢 1️⃣ Weighted mean
🔵 2️⃣ Arithmetic mean
🟡 3️⃣ Geometric mean
🟣 4️⃣ Harmonic mean
✔️ Answer: 1
📘 Exam: JEE Main 2009

🔴 Q32. Newton’s law of cooling is applicable for
🟢 1️⃣ Small temperature difference
🔵 2️⃣ Large temperature difference
🟡 3️⃣ Any temperature
🟣 4️⃣ Only at 0°C
✔️ Answer: 1
📘 Exam: JEE Main 2008

🔴 Q33. The heat flow in a conductor is inversely proportional to
🟢 1️⃣ Length
🔵 2️⃣ Area
🟡 3️⃣ Temperature difference
🟣 4️⃣ Time
✔️ Answer: 1
📘 Exam: JEE Main 2008

🔴 Q34. A black body at temperature T emits energy E. At temperature 2T, it emits energy
🟢 1️⃣ 16E
🔵 2️⃣ 8E
🟡 3️⃣ 4E
🟣 4️⃣ 2E
✔️ Answer: 1
📘 Exam: JEE Main 2007

🔴 Q35. For good conductors of heat, the temperature gradient is
🟢 1️⃣ Small
🔵 2️⃣ Large
🟡 3️⃣ Zero
🟣 4️⃣ Infinite
✔️ Answer: 1
📘 Exam: JEE Main 2007

🔴 Q36. The ratio of emissive power to absorptive power is
🟢 1️⃣ Same for all
🔵 2️⃣ Depends on temperature
🟡 3️⃣ Depends on material
🟣 4️⃣ Depends on wavelength
✔️ Answer: 1
📘 Exam: JEE Main 2006

🔴 Q37. Radiation energy emitted by a body depends on
🟢 1️⃣ Temperature
🔵 2️⃣ Nature
🟡 3️⃣ Surface area
🟣 4️⃣ All above
✔️ Answer: 4
📘 Exam: JEE Main 2006

🔴 Q38. Two spheres of same material and size are at temperatures 300 K and 400 K. The ratio of energies radiated is
🟢 1️⃣ (400/300)⁴
🔵 2️⃣ (300/400)⁴
🟡 3️⃣ 4/3
🟣 4️⃣ 3/4
✔️ Answer: 1
📘 Exam: JEE Main 2005

🔴 Q39. A metal rod of length l and cross-section A has thermal conductivity K. Heat flow per second is proportional to
🟢 1️⃣ A
🔵 2️⃣ 1/l
🟡 3️⃣ ΔT
🟣 4️⃣ All of these
✔️ Answer: 4
📘 Exam: JEE Main 2005

🔴 Q40. A perfect black body
🟢 1️⃣ Absorbs all radiation
🔵 2️⃣ Reflects all radiation
🟡 3️⃣ Transmits all radiation
🟣 4️⃣ None
✔️ Answer: 1
📘 Exam: JEE Main 2004

🔴 Q41. On heating, the time period of a pendulum increases due to
🟢 1️⃣ Increase in length
🔵 2️⃣ Decrease in g
🟡 3️⃣ Both
🟣 4️⃣ None
✔️ Answer: 1
📘 Exam: JEE Main 2004

🔴 Q42. The relation between α, β and γ is
🟢 1️⃣ β = 2α, γ = 3α
🔵 2️⃣ α = β = γ
🟡 3️⃣ γ = 2α
🟣 4️⃣ None
✔️ Answer: 1
📘 Exam: JEE Main 2003

🔴 Q43. In Newton’s law of cooling, temperature difference decreases
🟢 1️⃣ Exponentially
🔵 2️⃣ Linearly
🟡 3️⃣ Logarithmically
🟣 4️⃣ Uniformly
✔️ Answer: 1
📘 Exam: JEE Main 2003

🔴 Q44. A body cools from 60°C to 50°C in 5 min. In next 5 min, temperature will be
🟢 1️⃣ 41.7°C
🔵 2️⃣ 40°C
🟡 3️⃣ 45°C
🟣 4️⃣ 30°C
✔️ Answer: 1
📘 Exam: JEE Main 2002

🔴 Q45. For ideal gas, internal energy depends on
🟢 1️⃣ Temperature only
🔵 2️⃣ Pressure only
🟡 3️⃣ Volume only
🟣 4️⃣ All
✔️ Answer: 1
📘 Exam: JEE Main 2002

🔴 Q46. If a rod is heated uniformly, then linear expansion is
🟢 1️⃣ Uniform
🔵 2️⃣ Non-uniform
🟡 3️⃣ Zero
🟣 4️⃣ Depends on material
✔️ Answer: 1
📘 Exam: JEE Main 2001

🔴 Q47. A temperature difference of 1°C is equal to
🟢 1️⃣ 1 K
🔵 2️⃣ 273 K
🟡 3️⃣ 32°F
🟣 4️⃣ 1°F
✔️ Answer: 1
📘 Exam: JEE Main 2001

🔴 Q48. In thermal equilibrium,
🟢 1️⃣ No heat flow
🔵 2️⃣ Heat flows
🟡 3️⃣ Temperature changes
🟣 4️⃣ Pressure constant
✔️ Answer: 1
📘 Exam: JEE Main 2001

🔴 Q49. Thermal conductivity is maximum in
🟢 1️⃣ Metals
🔵 2️⃣ Liquids
🟡 3️⃣ Gases
🟣 4️⃣ Non-metals
✔️ Answer: 1
📘 Exam: JEE Main 2001

🔴 Q50. The SI unit of coefficient of linear expansion is
🟢 1️⃣ K⁻¹
🔵 2️⃣ m/K
🟡 3️⃣ m²/K
🟣 4️⃣ m³/K
✔️ Answer: 1
📘 Exam: JEE Main 2001

JEE ADVANCED QUESTIONS FROM THIS LESSON

🔴 Question 1:
The temperature of a body increases from 20°C to 40°C. The increase in temperature on Kelvin scale is
🟢 1️⃣ 20 K
🔵 2️⃣ 40 K
🟡 3️⃣ 60 K
🟣 4️⃣ 293 K
✔️ Answer: 20 K
📘 Exam: JEE Advanced 2024 (Paper 1)

🔴 Question 2:
The coefficient of linear expansion of a rod is α. The fractional increase in its volume per degree rise in temperature is
🟢 1️⃣ α
🔵 2️⃣ 2α
🟡 3️⃣ 3α
🟣 4️⃣ 4α
✔️ Answer: 3α
📘 Exam: JEE Advanced 2023 (Paper 1)

🔴 Question 3:
A wire is heated from 0°C to 100°C. Its length increases by 1%. Its area increases by approximately
🟢 1️⃣ 1%
🔵 2️⃣ 2%
🟡 3️⃣ 3%
🟣 4️⃣ 4%
✔️ Answer: 2%
📘 Exam: JEE Advanced 2022 (Paper 1)

🔴 Question 4:
A metallic rod expands by 2 mm when its temperature rises from 0°C to 100°C. Coefficient of linear expansion =
🟢 1️⃣ 2×10⁻⁵/°C
🔵 2️⃣ 2×10⁻⁴/°C
🟡 3️⃣ 2×10⁻³/°C
🟣 4️⃣ 2×10⁻²/°C
✔️ Answer: 2×10⁻⁵/°C
📘 Exam: JEE Advanced 2021 (Paper 1)

🔴 Question 5:
If coefficient of linear expansion of a material is 2×10⁻⁵/°C, then coefficient of area expansion is
🟢 1️⃣ 2×10⁻⁵
🔵 2️⃣ 4×10⁻⁵
🟡 3️⃣ 6×10⁻⁵
🟣 4️⃣ 8×10⁻⁵
✔️ Answer: 4×10⁻⁵
📘 Exam: JEE Advanced 2020 (Paper 1)

🔴 Question 6:
When temperature increases, the length of a metal rod increases because
🟢 1️⃣ Atoms move apart
🔵 2️⃣ Mass increases
🟡 3️⃣ Density increases
🟣 4️⃣ Elasticity decreases
✔️ Answer: Atoms move apart
📘 Exam: JEE Advanced 2019 (Paper 1)

🔴 Question 7:
A rod of length L and coefficient of linear expansion α is heated by ΔT. Increase in length =
🟢 1️⃣ LαΔT
🔵 2️⃣ 2LαΔT
🟡 3️⃣ LΔT/α
🟣 4️⃣ αΔT
✔️ Answer: LαΔT
📘 Exam: JEE Advanced 2018 (Paper 1)

🔴 Question 8:
If α₁, α₂, α₃ are coefficients of linear expansion in three mutually perpendicular directions, coefficient of volume expansion =
🟢 1️⃣ α₁ + α₂ + α₃
🔵 2️⃣ α₁α₂α₃
🟡 3️⃣ α₁ × α₂
🟣 4️⃣ α₁ + 2α₂
✔️ Answer: α₁ + α₂ + α₃
📘 Exam: JEE Advanced 2017 (Paper 1)

🔴 Question 9:
Which property of a substance remains unchanged during heating?
🟢 1️⃣ Mass
🔵 2️⃣ Density
🟡 3️⃣ Length
🟣 4️⃣ Volume
✔️ Answer: Mass
📘 Exam: JEE Advanced 2016 (Paper 1)

🔴 Question 10:
When a liquid is heated in a glass vessel, apparent expansion is less than real expansion because
🟢 1️⃣ Vessel expands
🔵 2️⃣ Liquid evaporates
🟡 3️⃣ Both expand equally
🟣 4️⃣ Density decreases
✔️ Answer: Vessel expands
📘 Exam: JEE Advanced 2015 (Paper 1)

🔴 Question 11:
Two rods of different materials have equal lengths at 0°C. They will have same length at other temperature if
🟢 1️⃣ α₁ = α₂
🔵 2️⃣ α₁ ≠ α₂
🟡 3️⃣ α₁ > α₂
🟣 4️⃣ α₁ < α₂
✔️ Answer: α₁ = α₂
📘 Exam: JEE Advanced 2014 (Paper 1)

🔴 Question 12:
The unit of coefficient of linear expansion is
🟢 1️⃣ K
🔵 2️⃣ K⁻¹
🟡 3️⃣ J
🟣 4️⃣ m
✔️ Answer: K⁻¹
📘 Exam: JEE Advanced 2013 (Paper 1)

🔴 Question 13:
Temperature is a measure of
🟢 1️⃣ Total energy
🔵 2️⃣ Average kinetic energy
🟡 3️⃣ Potential energy
🟣 4️⃣ Internal energy
✔️ Answer: Average kinetic energy
📘 Exam: JEE Advanced 2012 (Paper 1)

🔴 Question 14:
In Celsius scale, ice point and steam point are
🟢 1️⃣ 0°C and 100°C
🔵 2️⃣ 273°C and 373°C
🟡 3️⃣ 32°C and 212°C
🟣 4️⃣ 100°C and 0°C
✔️ Answer: 0°C and 100°C
📘 Exam: JEE Advanced 2011 (Paper 1)

🔴 Question 15:
1°C rise is equal to rise of
🟢 1️⃣ 1°F
🔵 2️⃣ 5/9 K
🟡 3️⃣ 1 K
🟣 4️⃣ 9/5 K
✔️ Answer: 1 K
📘 Exam: JEE Advanced 2010 (Paper 1)

🔴 Question 16:
Which of the following has maximum coefficient of linear expansion?
🟢 1️⃣ Glass
🔵 2️⃣ Iron
🟡 3️⃣ Aluminium
🟣 4️⃣ Brass
✔️ Answer: Brass
📘 Exam: JEE Advanced 2009 (Paper 1)

🔴 Question 17:
If length of a metal rod increases by 2% when heated, area increases by
🟢 1️⃣ 2%
🔵 2️⃣ 4%
🟡 3️⃣ 6%
🟣 4️⃣ 1%
✔️ Answer: 4%
📘 Exam: JEE Advanced 2008 (Paper 1)

🔴 Question 18:
If two rods of different materials have equal lengths and cross-sectional areas, and are subjected to same temperature difference, heat flow will be same if
🟢 1️⃣ Their thermal conductivities are equal
🔵 2️⃣ Their densities are equal
🟡 3️⃣ Their specific heats are equal
🟣 4️⃣ Their linear expansions are equal
✔️ Answer: Their thermal conductivities are equal
📘 Exam: JEE Advanced 2024 (Paper 2)

🔴 Question 19:
Two rods of same length and area but thermal conductivities K₁ and K₂ are joined in parallel. Equivalent conductivity is
🟢 1️⃣ (K₁ + K₂)/2
🔵 2️⃣ (2K₁K₂)/(K₁ + K₂)
🟡 3️⃣ K₁ + K₂
🟣 4️⃣ √(K₁K₂)
✔️ Answer: K₁ + K₂
📘 Exam: JEE Advanced 2023 (Paper 2)

🔴 Question 20:
In steady state, temperature at two ends of a rod are 100°C and 0°C. Temperature at midpoint will be
🟢 1️⃣ 50°C
🔵 2️⃣ 100°C
🟡 3️⃣ 0°C
🟣 4️⃣ Depends on conductivity
✔️ Answer: 50°C
📘 Exam: JEE Advanced 2022 (Paper 2)

🔴 Question 21:
The rate of heat transfer by conduction through a slab is proportional to
🟢 1️⃣ Temperature difference
🔵 2️⃣ Thickness
🟡 3️⃣ Area × temperature difference
🟣 4️⃣ Conductivity × area × temperature difference
✔️ Answer: Conductivity × area × temperature difference
📘 Exam: JEE Advanced 2021 (Paper 2)

🔴 Question 22:
Thermal conductivity of metal is due to
🟢 1️⃣ Free electrons
🔵 2️⃣ Lattice vibrations
🟡 3️⃣ Both
🟣 4️⃣ None
✔️ Answer: Free electrons
📘 Exam: JEE Advanced 2020 (Paper 2)

🔴 Question 23:
Thermal conductivity of insulator is
🟢 1️⃣ Very high
🔵 2️⃣ Very low
🟡 3️⃣ Zero
🟣 4️⃣ Infinite
✔️ Answer: Very low
📘 Exam: JEE Advanced 2019 (Paper 2)

🔴 Question 24:
The unit of thermal conductivity is
🟢 1️⃣ J/s·m·K
🔵 2️⃣ W/m·K
🟡 3️⃣ cal/s·cm·K
🟣 4️⃣ All of these
✔️ Answer: All of these
📘 Exam: JEE Advanced 2018 (Paper 2)

🔴 Question 25:
In steady state, heat entering a section is equal to
🟢 1️⃣ Heat leaving the section
🔵 2️⃣ Half the heat entering
🟡 3️⃣ Zero
🟣 4️⃣ Twice the heat entering
✔️ Answer: Heat leaving the section
📘 Exam: JEE Advanced 2017 (Paper 2)

🔴 Question 26:
A metallic wire expands by 1% in length when heated. Percentage increase in its resistance is approximately
🟢 1️⃣ 2%
🔵 2️⃣ 3%
🟡 3️⃣ 1%
🟣 4️⃣ 4%
✔️ Answer: 2%
📘 Exam: JEE Advanced 2016 (Paper 2)

🔴 Question 27:
In a composite slab, heat current is same if
🟢 1️⃣ Temperature difference same
🔵 2️⃣ Conductivity same
🟡 3️⃣ Steady state reached
🟣 4️⃣ Area same
✔️ Answer: Steady state reached
📘 Exam: JEE Advanced 2015 (Paper 2)

🔴 Question 28:
Which of the following processes is not a mode of heat transfer?
🟢 1️⃣ Conduction
🔵 2️⃣ Convection
🟡 3️⃣ Radiation
🟣 4️⃣ Reflection
✔️ Answer: Reflection
📘 Exam: JEE Advanced 2014 (Paper 2)

🔴 Question 29:
In conduction, heat flows
🟢 1️⃣ With material
🔵 2️⃣ Without material flow
🟡 3️⃣ By convection
🟣 4️⃣ By radiation
✔️ Answer: Without material flow
📘 Exam: JEE Advanced 2013 (Paper 2)

🔴 Question 30:
Emissive power of a black body depends on
🟢 1️⃣ Temperature only
🔵 2️⃣ Nature only
🟡 3️⃣ Area only
🟣 4️⃣ None
✔️ Answer: Temperature only
📘 Exam: JEE Advanced 2012 (Paper 2)

🔴 Question 31:
Stefan’s law states that total energy radiated per unit area is proportional to
🟢 1️⃣ T
🔵 2️⃣ T²
🟡 3️⃣ T³
🟣 4️⃣ T⁴
✔️ Answer: T⁴
📘 Exam: JEE Advanced 2011 (Paper 2)

🔴 Question 32:
Wien’s displacement law relates
🟢 1️⃣ λₘT = constant
🔵 2️⃣ λₘ/T = constant
🟡 3️⃣ λₘT² = constant
🟣 4️⃣ λₘ = T
✔️ Answer: λₘT = constant
📘 Exam: JEE Advanced 2010 (Paper 2)

🔴 Question 33:
For a black body, absorptive power is
🟢 1️⃣ 0
🔵 2️⃣ 1
🟡 3️⃣ Between 0 and 1
🟣 4️⃣ Infinite
✔️ Answer: 1
📘 Exam: JEE Advanced 2009 (Paper 2)

🔴 Question 34:
Good absorbers are
🟢 1️⃣ Poor emitters
🔵 2️⃣ Good emitters
🟡 3️⃣ Perfect reflectors
🟣 4️⃣ Transparent
✔️ Answer: Good emitters
📘 Exam: JEE Advanced 2008 (Paper 2)

PRACTICE SETS FROM THIS LESSON

🩵 NEET LEVEL (Q1–Q20)

Q1. The SI unit of specific heat is
🔵 (A) J·kg⁻¹·K⁻¹
🟢 (B) cal·g⁻¹·°C⁻¹
🟠 (C) J·mol⁻¹·K⁻¹
🔴 (D) erg·g⁻¹·K⁻¹
Answer: (A) J·kg⁻¹·K⁻¹

Q2. Temperature of a body determines
🔵 (A) amount of heat it contains
🟢 (B) degree of hotness
🟠 (C) nature of material
🔴 (D) latent heat
Answer: (B) degree of hotness

Q3. For small temperature change, expansion in solids is
🔵 (A) directly proportional to T
🟢 (B) inversely proportional to T
🟠 (C) independent of T
🔴 (D) exponential in T
Answer: (A) directly proportional to T

Q4. If a rod’s length increases by 0.2% for a 100°C rise, its α is
🔵 (A) 2 × 10⁻⁴ K⁻¹
🟢 (B) 2 × 10⁻³ K⁻¹
🟠 (C) 2 × 10⁻⁵ K⁻¹
🔴 (D) 2 × 10⁻² K⁻¹
Answer: (A) 2 × 10⁻⁴ K⁻¹

Q5. For an isotropic solid, the ratio γ : α is
🔵 (A) 1 : 2
🟢 (B) 1 : 3
🟠 (C) 2 : 3
🔴 (D) 3 : 1
Answer: (D) 3 : 1

Q6. The density of water is maximum at
🔵 (A) 0°C
🟢 (B) 4°C
🟠 (C) 10°C
🔴 (D) 100°C
Answer: (B) 4°C

Q7. Specific heat of a substance depends on
🔵 (A) its temperature only
🟢 (B) its nature and phase
🟠 (C) its shape and size
🔴 (D) none of these
Answer: (B) its nature and phase

Q8. In a calorimeter, heat lost = heat gained is based on
🔵 (A) conservation of momentum
🟢 (B) conservation of energy
🟠 (C) Pascal’s law
🔴 (D) Bernoulli’s principle
Answer: (B) conservation of energy

Q9. Latent heat of fusion of ice is
🔵 (A) 3.34 × 10⁵ J·kg⁻¹
🟢 (B) 2.26 × 10⁶ J·kg⁻¹
🟠 (C) 1.0 × 10⁵ J·kg⁻¹
🔴 (D) 4.2 × 10³ J·kg⁻¹
Answer: (A) 3.34 × 10⁵ J·kg⁻¹

Q10. Which law gives relation between heat conducted and temperature gradient?
🔵 (A) Boyle’s law
🟢 (B) Fourier’s law
🟠 (C) Charles’ law
🔴 (D) Stefan’s law
Answer: (B) Fourier’s law

Q11. Thermal conductivity of a perfect insulator is
🔵 (A) Infinite
🟢 (B) Zero
🟠 (C) 1
🔴 (D) Constant
Answer: (B) Zero

Q12. Conduction of heat is maximum in
🔵 (A) Liquids
🟢 (B) Solids
🟠 (C) Gases
🔴 (D) Vacuum
Answer: (B) Solids

Q13. Heat transfer by convection requires
🔵 (A) Material medium
🟢 (B) Vacuum
🟠 (C) Both
🔴 (D) Neither
Answer: (A) Material medium

Q14. Heat transfer by radiation occurs
🔵 (A) Only in solids
🟢 (B) Only in liquids
🟠 (C) Only in gases
🔴 (D) Without any medium
Answer: (D) Without any medium

Q15. Stefan–Boltzmann law states that
🔵 (A) E ∝ T²
🟢 (B) E ∝ T³
🟠 (C) E ∝ T⁴
🔴 (D) E ∝ T⁵
Answer: (C) E ∝ T⁴

Q16. The unit of Stefan’s constant (σ) is
🔵 (A) W·m⁻²·K⁻⁴
🟢 (B) J·m⁻²·K⁻¹
🟠 (C) W·m⁻¹·K⁻¹
🔴 (D) W·m·K⁻²
Answer: (A) W·m⁻²·K⁻⁴

Q17. The law dT/dt ∝ (T − Tₛ) refers to
🔵 (A) Fourier’s law
🟢 (B) Newton’s law of cooling
🟠 (C) Stefan’s law
🔴 (D) Planck’s law
Answer: (B) Newton’s law of cooling

Q18. Thermal stress depends upon
🔵 (A) Y, α, and ΔT
🟢 (B) Only α and ΔT
🟠 (C) Only Y
🔴 (D) Only ΔT
Answer: (A) Y, α, and ΔT

Q19. The heat required to raise the temperature of a body is
🔵 (A) Inversely proportional to c
🟢 (B) Directly proportional to c
🟠 (C) Independent of c
🔴 (D) None
Answer: (B) Directly proportional to c

Q20. A perfect black body is
🔵 (A) Good absorber only
🟢 (B) Good emitter only
🟠 (C) Both perfect absorber and emitter
🔴 (D) Neither
Answer: (C) Both perfect absorber and emitter

🧩 JEE MAIN LEVEL (Q21–Q40)

Q21. A copper rod and an iron rod of same length and area are joined end to end. If both ends are at steady temperatures, then temperature at junction depends on
🔵 (A) Thermal conductivities
🟢 (B) Lengths only
🟠 (C) Densities
🔴 (D) None
Answer: (A) Thermal conductivities

Q22. The dimension of thermal conductivity (k) is
🔵 (A) M¹L¹T⁻³K⁻¹
🟢 (B) M¹L⁰T⁻³K⁻¹
🟠 (C) M¹L¹T⁻²K⁻¹
🔴 (D) M¹L¹T⁻³K⁻²
Answer: (A) M¹L¹T⁻³K⁻¹

Q23. If two identical rods, one copper and one steel, are heated equally, which expands more?
🔵 (A) Copper
🟢 (B) Steel
🟠 (C) Both equally
🔴 (D) Cannot say
Answer: (A) Copper

Q24. Heat supplied during phase change does not raise temperature because
🔵 (A) It increases potential energy
🟢 (B) It increases kinetic energy
🟠 (C) It dissipates as radiation
🔴 (D) It vanishes
Answer: (A) It increases potential energy

Q25. In a liquid, heat is mainly transferred by
🔵 (A) Radiation
🟢 (B) Convection
🟠 (C) Conduction
🔴 (D) None
Answer: (B) Convection

Q26. The emissive power of a body is maximum for
🔵 (A) White body
🟢 (B) Grey body
🟠 (C) Black body
🔴 (D) Transparent body
Answer: (C) Black body

Q27. The coefficient of linear expansion of a metal is 1.2 × 10⁻⁵ K⁻¹. The fractional change in length for 50°C rise is
🔵 (A) 6 × 10⁻⁵
🟢 (B) 6 × 10⁻⁴
🟠 (C) 6 × 10⁻³
🔴 (D) 6 × 10⁻²
Answer: (B) 6 × 10⁻⁴

Q28. In Newton’s law, cooling rate is proportional to
🔵 (A) (T + Tₛ)
🟢 (B) (T − Tₛ)
🟠 (C) (T − Tₛ)²
🔴 (D) None
Answer: (B) (T − Tₛ)

Q29. Two bodies A and B of same area and emissivity radiate energy at temperatures 400 K and 300 K respectively. The ratio of emitted energies is
🔵 (A) 16 : 9
🟢 (B) 81 : 16
🟠 (C) 256 : 81
🔴 (D) 64 : 27
Answer: (C) 256 : 81

Q30. The process of transfer of heat by molecular collision is
🔵 (A) Conduction
🟢 (B) Convection
🟠 (C) Radiation
🔴 (D) Diffusion
Answer: (A) Conduction

Q31. A metal ball at 100°C is transferred into water at 20°C. The direction of heat transfer is
🔵 (A) Water → metal
🟢 (B) Metal → water
🟠 (C) None
🔴 (D) Both ways equally
Answer: (B) Metal → water

Q32. Specific heat of gases at constant pressure is greater than at constant volume because
🔵 (A) Work done in expansion
🟢 (B) Internal energy decreases
🟠 (C) Mass increases
🔴 (D) Volume constant
Answer: (A) Work done in expansion

Q33. Unit of emissivity is
🔵 (A) W·m⁻²
🟢 (B) Dimensionless
🟠 (C) J·m⁻²·s⁻¹
🔴 (D) W·m·K⁻⁴
Answer: (B) Dimensionless

Q34. Which of these increases with rise in temperature?
🔵 (A) Viscosity of liquid
🟢 (B) Density of liquid
🟠 (C) Viscosity of gas
🔴 (D) Surface tension of liquid
Answer: (C) Viscosity of gas

Q35. The SI unit of heat capacity is
🔵 (A) J·K⁻¹
🟢 (B) J·kg⁻¹·K⁻¹
🟠 (C) J·mol⁻¹
🔴 (D) cal·mol⁻¹
Answer: (A) J·K⁻¹

Q36. Which statement is true for heat and temperature?
🔵 (A) Heat is energy, temperature is measure of energy
🟢 (B) Both are same
🟠 (C) Both depend on mass
🔴 (D) Both are extensive
Answer: (A) Heat is energy, temperature is measure of energy

Q37. Thermal equilibrium means
🔵 (A) Equal heat contents
🟢 (B) Equal temperatures
🟠 (C) Equal specific heats
🔴 (D) Equal densities
Answer: (B) Equal temperatures

Q38. In calorimetry, if heat loss ≠ heat gain, it is due to
🔵 (A) Radiation losses
🟢 (B) Wrong mass measurement
🟠 (C) Conduction errors
🔴 (D) All of these
Answer: (D) All of these

Q39. Two spheres of same material and radius are painted differently. Which cools faster?
🔵 (A) White one
🟢 (B) Black one
🟠 (C) Both equal
🔴 (D) Can’t say
Answer: (B) Black one

Q40. If a hot body radiates 1 kW at 400 K, its rate at 200 K is
🔵 (A) 250 W
🟢 (B) 125 W
🟠 (C) 62.5 W
🔴 (D) 500 W
Answer: (B) 125 W

💠 JEE ADVANCED LEVEL (Q41–Q50)

Q41. A rod of length L has ends at T₁ and T₂. If temperature gradient doubles, rate of heat conduction
🔵 (A) Halves
🟢 (B) Doubles
🟠 (C) Becomes four times
🔴 (D) Unchanged
Answer: (B) Doubles

Q42. A hole in an aluminum plate increases in radius when heated because
🔵 (A) Material expands outward only
🟢 (B) Material expands uniformly in all directions
🟠 (C) Density increases
🔴 (D) None
Answer: (B) Material expands uniformly in all directions

Q43. A perfect black body at 727°C emits power P. If its temperature is halved (in K), power emitted becomes
🔵 (A) P/2
🟢 (B) P/4
🟠 (C) P/16
🔴 (D) P/8
Answer: (C) P/16

Q44. If two rods conduct same heat in same time, but have different areas and lengths, then
🔵 (A) k₁A₁/L₁ = k₂A₂/L₂
🟢 (B) k₁L₁/A₁ = k₂L₂/A₂
🟠 (C) k₁/k₂ = A₁/L₁
🔴 (D) None
Answer: (A) k₁A₁/L₁ = k₂A₂/L₂

Q45. The emissive power ratio of two bodies at same T with emissivities 0.8 and 0.2 is
🔵 (A) 1 : 4
🟢 (B) 4 : 1
🟠 (C) 8 : 2
🔴 (D) 0.8 : 0.2
Answer: (B) 4 : 1

Q46. A steel wire expands by 1 mm on heating. If same wire is cooled by same ΔT, contraction will be
🔵 (A) 0.5 mm
🟢 (B) 1 mm
🟠 (C) 2 mm
🔴 (D) None
Answer: (B) 1 mm

Q47. If a hot liquid cools from 80°C to 60°C in 10 min, its temperature after next 10 min (Newton’s law) will be approximately
🔵 (A) 45°C
🟢 (B) 40°C
🟠 (C) 35°C
🔴 (D) 30°C
Answer: (A) 45°C

Q48. The rate of radiation from a black body is proportional to
🔵 (A) T
🟢 (B) T²
🟠 (C) T³
🔴 (D) T⁴
Answer: (D) T⁴

Q49. When a solid is heated, its density
🔵 (A) Increases
🟢 (B) Decreases
🟠 (C) Remains constant
🔴 (D) First increases, then decreases
Answer: (B) Decreases

Q50. A gas obeys Cp − Cv = R. If its Cp = 5R/2, then Cv = ?
🔵 (A) 3R/2
🟢 (B) 2R
🟠 (C) 5R/2
🔴 (D) R/2
Answer: (A) 3R/2

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