NEET Physics: Heat, Thermodynamics and Kinetic Theory · Chapter 1

Thermal Properties of Matter

What to remember

Heat is energy in transit because of a temperature difference; temperature is the degree of hotness. Q = mcΔT for a change of temperature and Q = mL for a change of state (temperature stays constant during the change of state).
Linear, area and volume expansion coefficients of an isotropic solid are in the ratio α : β : γ = 1 : 2 : 3. Water is anomalous: it contracts on heating from 0 °C to 4 °C and has its maximum density at 4 °C.
Conduction follows Q/t = KAΔT/L. For slabs in series the heat current is the same in each slab; for slabs in parallel the heat currents add.
Blackbody radiation: power radiated P = σAT⁴ (Stefan-Boltzmann law) and λm T = b (Wien's displacement law). Newton's law of cooling: rate of cooling is proportional to the excess of the body's temperature over its surroundings (for small differences).

Temperature and heat

Temperature tells how hot or cold a body is. Heat is the energy that flows from a hotter body to a colder body because of the temperature difference. Heat is measured in joule (J). One calorie = 4.186 J.

Three scales are used. The Celsius scale has the ice point at 0 °C and the steam point at 100 °C. The Fahrenheit scale has them at 32 °F and 212 °F. The Kelvin scale is the SI scale; its zero is absolute zero.

Fixed point	Celsius	Fahrenheit	Kelvin
Ice point	0	32	273.15
Steam point	100	212	373.15
Triple point of water	0.01	about 32.02	273.16
Absolute zero	−273.15	−459.67	0

Conversions:

C/5 = (F − 32)/9
T (kelvin) = t (Celsius) + 273.15
A change of 1 K equals a change of 1 °C. A change of 1 °C equals a change of 1.8 °F.

Ideal-gas equation and absolute temperature

A constant-volume gas thermometer uses the fact that the pressure of a low-density gas at constant volume is proportional to its absolute temperature. If the pressure at the triple point of water is P_tr, then T = 273.16 K × (P/P_tr). Extending the straight-line graph of pressure against temperature backwards, the pressure becomes zero at −273.15 °C. This temperature is absolute zero.

The ideal-gas equation is PV = nRT, with R = 8.314 J mol⁻¹ K⁻¹. Here P is pressure in pascal, V is volume in m³, n is the number of moles and T is the absolute temperature in kelvin. At constant volume, P₁/T₁ = P₂/T₂. Temperature in these equations is always in kelvin.

Thermal expansion

Most substances expand on heating. For a small rise ΔT:

Type	Formula	Coefficient
Linear (rod)	ΔL = αLΔT	α, unit K⁻¹
Area (plate)	ΔA = βAΔT	β = 2α
Volume	ΔV = γVΔT	γ = 3α

Approximate values of α in 10⁻⁶ K⁻¹: aluminium 25, brass 19, copper 17, iron 12, gold 14, Pyrex glass 3.2. For gases at constant pressure, γ = 1/T for an ideal gas, about 3.67 × 10⁻³ K⁻¹ near 0 °C.

Useful facts:

A hole in a metal plate expands on heating exactly as if it were made of the same metal. The hole gets larger.
A bimetallic strip is made of two metals riveted together, for example brass and iron. On heating, the metal with the larger α (brass) becomes longer, so it lies on the outer, convex side of the bend.
Metal rails and bridges are laid with small gaps, and a metal tyre is fitted on a wheel by heating it, because of expansion.

Anomalous expansion of water. From 0 °C to 4 °C water contracts when heated, so its density rises. At 4 °C its density is maximum, about 1000 kg m⁻³. Above 4 °C it expands like other liquids. Ice is less dense than water, so ice floats. In a cold lake the water at 4 °C sinks to the bottom, and ice forms at the top first. Fish and plants survive in the water below the ice.

Specific heat capacity and calorimetry

Heat capacity of a body S = Q/ΔT (J K⁻¹). It depends on the mass and the material.

Specific heat capacity c = Q/(mΔT) = (1/m)(ΔQ/ΔT), in J kg⁻¹ K⁻¹. It depends only on the material (and on temperature slightly).

Molar specific heat capacity C = Q/(nΔT), in J mol⁻¹ K⁻¹.

Substance	c (J kg⁻¹ K⁻¹), about
Water	4186
Ice	2100
Aluminium	900
Iron	450
Copper	386
Mercury	140
Lead	130

Water has a very high specific heat. So it heats and cools slowly, and it is used as a coolant. Land heats faster than the sea in the day, so a sea breeze blows from the sea to the land. At night a land breeze blows from the land to the sea.

Calorimetry and the principle of mixtures. When bodies at different temperatures are mixed in an insulated container, heat lost by the hot bodies = heat gained by the cold bodies. The final temperature lies between the initial temperatures.

Change of state and latent heat

Matter changes state at a fixed temperature while heat is absorbed or given out. The heat per unit mass needed is the latent heat: Q = mL.

Quantity	Value (about)
Latent heat of fusion of ice, L_f	3.33 × 10⁵ J kg⁻¹ (80 cal g⁻¹)
Latent heat of vaporisation of water, L_v	2.26 × 10⁶ J kg⁻¹ (540 cal g⁻¹)
Melting point of ice	0 °C
Boiling point of water at 1 atm	100 °C

Heating curve of water in words. Start with ice at a temperature below 0 °C. The temperature rises (slope depends on c of ice) until 0 °C. Then it stays at 0 °C while the ice melts. It then rises as water until 100 °C. It stays at 100 °C while the water boils. Then the steam temperature rises again. The sequence is: ice rising → flat (melting) → water rising → flat (boiling) → steam rising. The flat part at boiling is longer because L_v is larger than L_f. The slope of the water part is gentler than that of ice or steam because c of water is larger.

Triple point. The triple point is the single condition of pressure and temperature at which the solid, liquid and vapour phases of a substance coexist in equilibrium. For water it is 273.16 K (0.01 °C) at a pressure of about 611 Pa. It is used as the fixed point of the Kelvin scale.

A burn from steam at 100 °C is worse than one from water at 100 °C, because steam gives out the large latent heat when it condenses.

Heat transfer

Conduction. Heat flows through a material from the hot end to the cold end without bulk motion of the material. In steady state for a slab of area A and thickness L with end temperatures T₁ > T₂:

Q/t = H = KA(T₁ − T₂)/L

K is the thermal conductivity, in W m⁻¹ K⁻¹. Metals have high K; wood, air and wool have low K. A metal spoon feels colder than a wooden one at the same temperature because metal conducts heat away from the hand faster.

Thermal resistance R = L/(KA). Then H = ΔT/R.

Slabs in series (same area, same heat current): R = R₁ + R₂. The equivalent conductivity is K = (L₁ + L₂)/(L₁/K₁ + L₂/K₂). The temperature drop across each slab is H × R of that slab; the larger resistance has the larger drop.
Slabs in parallel (same temperature difference): H = H₁ + H₂, so K_eq A = K₁A₁ + K₂A₂.

Convection. Heat is carried by the bulk movement of a fluid. In natural convection the motion is caused by differences in density; in forced convection a pump or fan drives it. Examples: sea breeze, land breeze, heating of water in a kettle, and trade winds.

Radiation. Heat is carried by electromagnetic waves. It needs no material medium and travels at the speed of light. This is how heat from the Sun reaches the Earth.

Blackbody radiation

A blackbody absorbs all radiation that falls on it. It is also the best possible emitter at a given temperature. In general, good absorbers are good emitters (and poor absorbers are poor emitters). The emissivity e is a number between 0 and 1; e = 1 for a blackbody.

Stefan-Boltzmann law. Power radiated by a body of surface area A at absolute temperature T is H = eσAT⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. If the surroundings are at T₀, the net power lost is eσA(T⁴ − T₀⁴).

Wien's displacement law. λm T = b, where λm is the wavelength at which the emitted power is maximum and b = 2.9 × 10⁻³ m K. As the temperature rises, λm shifts to shorter wavelengths. A very hot body looks bluish-white; a cooler body looks red. For the Sun the surface temperature of about 6000 K gives λm in the visible region.

Newton's law of cooling

For a small temperature excess, the rate of loss of heat is proportional to the excess of the body's temperature T over the surroundings' temperature T₀:

dT/dt = −k(T − T₀)

For a body cooling from T₁ to T₂ in time t, a working form is

(T₁ − T₂)/t = k[(T₁ + T₂)/2 − T₀]

The cooling curve of temperature against time is a falling curve whose slope (rate of cooling) becomes smaller as the body approaches T₀. The temperature never goes below T₀.

Worked examples

Example 1 (heat for several stages). Find the heat needed to change 100 g of ice at −10 °C into steam at 100 °C. Use c_ice = 2100, c_water = 4186 J kg⁻¹ K⁻¹, L_f = 3.33 × 10⁵, L_v = 2.26 × 10⁶ J kg⁻¹.

Warm ice: 0.1 × 2100 × 10 = 2100 J
Melt ice: 0.1 × 3.33 × 10⁵ = 33 300 J
Warm water: 0.1 × 4186 × 100 = 41 860 J
Boil water: 0.1 × 2.26 × 10⁶ = 226 000 J
Total = 303 260 J, about 3.03 × 10⁵ J.

Example 2 (principle of mixtures). 200 g of water at 80 °C is mixed with 300 g of water at 20 °C. Heat lost = heat gained: 200 (80 − T) = 300 (T − 20). So 16 000 − 200T = 300T − 6000, giving 500T = 22 000 and T = 44 °C.

Example 3 (slabs in series). Slab A has L = 0.1 m and K = 200 W m⁻¹ K⁻¹. Slab B has L = 0.2 m and K = 100 W m⁻¹ K⁻¹. They have the same area. The outer faces are at 100 °C (A side) and 0 °C (B side). Resistance per unit area: A = 0.1/200 = 5 × 10⁻⁴; B = 0.2/100 = 2 × 10⁻³ (m² K W⁻¹). Total = 2.5 × 10⁻³. Heat flow per unit area = 100/(2.5 × 10⁻³) = 40 000 W m⁻². Drop across A = 40 000 × 5 × 10⁻⁴ = 20 °C. So the interface is at 100 − 20 = 80 °C.

Example 4 (Stefan-Boltzmann). A blackbody sphere of surface area 0.01 m² is at 1000 K. P = σAT⁴ = 5.67 × 10⁻⁸ × 0.01 × 10¹² = 567 W.

Formula summary

Quantity	Formula	Unit
Fahrenheit–Celsius	C/5 = (F − 32)/9	°C, °F
Kelvin	T = t + 273.15	K
Ideal gas	PV = nRT	Pa m³ = J
Linear expansion	ΔL = αLΔT	m
Area, volume expansion	β = 2α, γ = 3α	K⁻¹
Heat for temperature change	Q = mcΔT	J
Heat for change of state	Q = mL	J
Conduction	H = KA(T₁ − T₂)/L	W
Thermal resistance	R = L/(KA)	K W⁻¹
Stefan-Boltzmann	H = eσAT⁴	W
Wien	λm T = b	m K
Newton's cooling	dT/dt = −k(T − T₀)	K s⁻¹

NEET traps

1. Heat and temperature are not the same; heat is energy in J, temperature is a measure of hotness in K.
2. Specific heat capacity does not depend on mass; heat capacity does.
3. A hole in a heated plate gets larger; it does not shrink.
4. β = 2α and γ = 3α are for isotropic solids; do not use α² or α³.
5. In Stefan's law T must be in kelvin, and the power depends on T⁴, not T².
6. In Wien's law a hotter body has a shorter λm, not a longer one.
7. During melting and boiling the temperature stays constant although heat is being supplied.
8. In series the heat current is equal and the temperature drops differ; in parallel the temperature difference is equal and the heat currents differ.
9. Water is densest at 4 °C, not at 0 °C.
10. Newton's law of cooling uses the excess over the surroundings, not the temperature itself.

One-liners

1. 0 °C = 32 °F = 273.15 K.
2. The triple point of water is 273.16 K.
3. Absolute zero is −273.15 °C.
4. γ = 3α and β = 2α for isotropic solids.
5. Water has maximum density at 4 °C.
6. c of water is about 4186 J kg⁻¹ K⁻¹.
7. 1 cal = 4.186 J.
8. L_f of ice is about 3.33 × 10⁵ J kg⁻¹.
9. L_v of water is about 2.26 × 10⁶ J kg⁻¹.
10. Conduction needs a medium but no bulk motion; radiation needs no medium.
11. Thermal resistance of a slab is L/(KA).
12. A blackbody absorbs and emits the maximum possible radiation.
13. σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.
14. Wien's constant b = 2.9 × 10⁻³ m K.
15. Doubling the absolute temperature of a radiator raises its power 16 times.

Practice questions

A temperature of 77 °F corresponds to which Celsius temperature?
1. 43 °C
2. 45 °C
3. 25 °C
4. 52 °C
Answer
C. 25 °C
C = (F − 32) × 5/9 = (77 − 32) × 5/9 = 25 °C. Check: 25 × 1.8 + 32 = 77.
The triple point of water on the Kelvin scale is
1. 373.16 K
2. 0.01 K
3. 100 K
4. 273.16 K
Answer
D. 273.16 K
The triple point of water is 0.01 °C, which is 273.16 K, and it is the fixed point of the Kelvin scale.
An iron rod 2 m long at 20 °C is heated to 120 °C. Take α for iron as 12 × 10⁻⁶ K⁻¹. The increase in length is
1. 4.8 mm
2. 2.4 mm
3. 1.2 mm
4. 0.24 mm
Answer
B. 2.4 mm
ΔL = αLΔT = 12 × 10⁻⁶ × 2 × 100 = 2.4 × 10⁻³ m = 2.4 mm.
A solid has a coefficient of linear expansion of 2 × 10⁻⁵ K⁻¹. Its coefficient of volume expansion is
1. 6 × 10⁻⁵ K⁻¹
2. 8 × 10⁻⁵ K⁻¹
3. 2 × 10⁻⁵ K⁻¹
4. 4 × 10⁻⁵ K⁻¹
Answer
A. 6 × 10⁻⁵ K⁻¹
γ = 3α = 3 × 2 × 10⁻⁵ = 6 × 10⁻⁵ K⁻¹ (β = 2α would give 4 × 10⁻⁵).
Water has its maximum density at
1. 4 °C
2. 0 °C
3. 100 °C
4. −4 °C
Answer
A. 4 °C
Water contracts from 0 °C to 4 °C and expands above 4 °C, so the density is greatest at 4 °C.
The specific heat capacity of water is taken as 4200 J kg⁻¹ K⁻¹. The heat needed to raise the temperature of 500 g of water from 20 °C to 60 °C is
1. 42 000 J
2. 8400 J
3. 168 000 J
4. 84 000 J
Answer
D. 84 000 J
Q = mcΔT = 0.5 × 4200 × 40 = 84 000 J. Check in calories: 500 g × 1 cal g⁻¹ °C⁻¹ × 40 = 20 000 cal ≈ 84 000 J.
The latent heat of fusion of ice is 3.33 × 10⁵ J kg⁻¹. The heat needed to melt 200 g of ice at 0 °C is
1. 33 300 J
2. 66 600 J
3. 666 000 J
4. 6660 J
Answer
B. 66 600 J
Q = mL = 0.2 × 3.33 × 10⁵ = 6.66 × 10⁴ J = 66 600 J.
Which mode of heat transfer does not need a material medium?
1. Conduction
2. Radiation
3. Convection
4. Conduction and convection both
Answer
B. Radiation
Radiation is carried by electromagnetic waves and can travel through vacuum, as sunlight does.
The absolute temperature of a blackbody is doubled. The power it radiates becomes
1. 8 times
2. 2 times
3. 16 times
4. 4 times
Answer
C. 16 times
P ∝ T⁴, so (2)⁴ = 16 times.
Take Wien's constant as 2.9 × 10⁻³ m K. The wavelength of maximum emission from a blackbody at 6000 K is about
1. 4830 nm
2. 48.3 nm
3. 483 nm
4. 966 nm
Answer
C. 483 nm
λm = b/T = 2.9 × 10⁻³/6000 = 4.83 × 10⁻⁷ m = 483 nm.
A metal rod of length 1 m and cross-section 2 × 10⁻⁴ m² has thermal conductivity 400 W m⁻¹ K⁻¹. Its ends are kept at 100 °C and 0 °C. The steady heat current is
1. 0.8 W
2. 80 W
3. 4 W
4. 8 W
Answer
D. 8 W
H = KAΔT/L = 400 × 2 × 10⁻⁴ × 100/1 = 8 W.
The SI unit of specific heat capacity is
1. J kg⁻¹ K⁻¹
2. J K⁻¹
3. J kg⁻¹
4. J kg K⁻¹
Answer
A. J kg⁻¹ K⁻¹
c = Q/(mΔT), so its unit is J kg⁻¹ K⁻¹.
300 g of water at 90 °C is mixed with 200 g of water at 15 °C in an insulated vessel. The final temperature is
1. 75 °C
2. 60 °C
3. 48 °C
4. 52.5 °C
Answer
B. 60 °C
300 (90 − T) = 200 (T − 15) gives 500T = 30 000, so T = 60 °C.
50 g of ice at 0 °C is dropped into 200 g of water at 40 °C in an insulated vessel. Take c of water = 4200 J kg⁻¹ K⁻¹ and L of fusion = 3.36 × 10⁵ J kg⁻¹. The final temperature is
1. 16 °C
2. 8 °C
3. 24 °C
4. 20 °C
Answer
A. 16 °C
Heat from water cooling to 0 °C = 0.2 × 4200 × 40 = 33 600 J. Melting uses 16 800 J. The remaining 16 800 J warms 250 g: ΔT = 16 800/(0.25 × 4200) = 16 °C.
A gas in a rigid vessel has a pressure of 2 atm at 27 °C. The pressure when it is heated to 127 °C is
1. 9.4 atm
2. 4 atm
3. 8/3 atm (about 2.67 atm)
4. 1.5 atm
Answer
C. 8/3 atm (about 2.67 atm)
At constant volume P₂ = P₁T₂/T₁ = 2 × 400/300 = 8/3 atm. Temperatures must be in kelvin.
Given below are two statements: Statement I: On heating from 0 °C to 4 °C, water contracts. Statement II: The density of water is maximum at 4 °C.
1. Both Statement I and Statement II are incorrect
2. Both Statement I and Statement II are correct
3. Statement I is correct but Statement II is incorrect
4. Statement I is incorrect but Statement II is correct
Answer
B. Both Statement I and Statement II are correct
Contraction from 0 °C to 4 °C raises the density, which peaks at 4 °C. Both are correct.
Given below are two statements: Statement I: The coefficient of areal expansion of an isotropic solid is twice its coefficient of linear expansion. Statement II: A circular hole in a metal plate becomes smaller when the plate is heated.
1. Both Statement I and Statement II are correct
2. Statement I is correct but Statement II is incorrect
3. Both Statement I and Statement II are incorrect
4. Statement I is incorrect but Statement II is correct
Answer
B. Statement I is correct but Statement II is incorrect
β = 2α is correct. The hole expands as if it were made of the plate material, so Statement II is incorrect.
Given below are two statements: Statement I: The latent heat of vaporisation of water is greater than its latent heat of fusion. Statement II: The temperature of boiling water stays constant while heat is supplied.
1. Both Statement I and Statement II are incorrect
2. Statement I is correct but Statement II is incorrect
3. Statement I is incorrect but Statement II is correct
4. Both Statement I and Statement II are correct
Answer
D. Both Statement I and Statement II are correct
L_v is about 2.26 × 10⁶ J kg⁻¹ and L_f about 3.33 × 10⁵ J kg⁻¹. During a change of state the temperature is constant.
Given below are two statements: Statement I: The specific heat capacity of a body depends on its mass. Statement II: The heat capacity of a body depends on its mass.
1. Both Statement I and Statement II are correct
2. Statement I is incorrect but Statement II is correct
3. Both Statement I and Statement II are incorrect
4. Statement I is correct but Statement II is incorrect
Answer
B. Statement I is incorrect but Statement II is correct
Specific heat capacity depends on the material only; heat capacity S = mc depends on mass.
Which of the following statements are correct? 1. In conduction, heat flows without bulk movement of the material. 2. In convection, heat is carried by the bulk movement of a fluid. 3. Radiation needs a material medium.
1. 1 and 3 only
2. 2 and 3 only
3. 1 and 2 only
4. 1, 2 and 3
Answer
C. 1 and 2 only
Statements 1 and 2 describe conduction and convection correctly. Radiation needs no medium, so 3 is wrong.
Which of the following statements are correct? 1. A perfect blackbody absorbs all radiation falling on it. 2. The wavelength of maximum emission shifts to shorter values when the temperature rises. 3. The total power radiated per unit area of a blackbody is proportional to T².
1. 2 and 3 only
2. 1 and 3 only
3. 1, 2 and 3
4. 1 and 2 only
Answer
D. 1 and 2 only
Statements 1 and 2 are correct. Stefan's law gives power per unit area ∝ T⁴, so 3 is wrong.
Given below are two statements: Statement I: A good absorber of radiation is also a good emitter at the same temperature. Statement II: A polished silver surface radiates more than a lamp-black surface at the same temperature.
1. Both Statement I and Statement II are correct
2. Statement I is correct but Statement II is incorrect
3. Both Statement I and Statement II are incorrect
4. Statement I is incorrect but Statement II is correct
Answer
B. Statement I is correct but Statement II is incorrect
Good absorbers are good emitters, so lamp-black radiates more than polished silver. Statement II is incorrect.
Given below are two statements: Statement I: Two slabs joined in series carry the same heat current in the steady state. Statement II: The slab with the larger thermal conductivity always has the larger temperature drop.
1. Statement I is correct but Statement II is incorrect
2. Both Statement I and Statement II are correct
3. Both Statement I and Statement II are incorrect
4. Statement I is incorrect but Statement II is correct
Answer
A. Statement I is correct but Statement II is incorrect
In series H is equal. The drop is H × R, so the slab with the larger resistance has the larger drop; this is not decided by K alone.
Given below are two statements: Statement I: Absolute zero is −273.15 °C. Statement II: A one-kelvin change in temperature is not equal to a one-degree Celsius change.
1. Both Statement I and Statement II are correct
2. Both Statement I and Statement II are incorrect
3. Statement I is correct but Statement II is incorrect
4. Statement I is incorrect but Statement II is correct
Answer
C. Statement I is correct but Statement II is incorrect
Absolute zero is −273.15 °C. The size of a kelvin equals the size of a Celsius degree, so Statement II is incorrect.
Given below are two statements: Statement I: A body cooling by Newton's law takes less time to cool from 80 °C to 70 °C than from 70 °C to 60 °C, when the surroundings are at 30 °C. Statement II: The rate of cooling decreases as the excess temperature over the surroundings decreases.
1. Both Statement I and Statement II are incorrect
2. Both Statement I and Statement II are correct
3. Statement I is correct but Statement II is incorrect
4. Statement I is incorrect but Statement II is correct
Answer
B. Both Statement I and Statement II are correct
The excess is larger in the first interval, so cooling is faster there and takes less time. Both are correct and II explains I.
Assertion (A): A metal spoon feels colder than a wooden spoon at the same temperature. Reason (R): Metals have a higher thermal conductivity than wood.
1. Both A and R are true but R is not the correct explanation of A
2. A is true but R is false
3. Both A and R are true and R is the correct explanation of A
4. A is false but R is true
Answer
C. Both A and R are true and R is the correct explanation of A
Metal conducts heat away from the hand faster, so it feels colder. R explains A.
Assertion (A): A blackbody is the best radiator at a given temperature. Reason (R): A blackbody reflects all the radiation that falls on it.
1. A is true but R is false
2. Both A and R are true and R is the correct explanation of A
3. Both A and R are true but R is not the correct explanation of A
4. A is false but R is true
Answer
A. A is true but R is false
A is true because a blackbody has emissivity 1. R is false: a blackbody absorbs all radiation and reflects none.
Assertion (A): The temperature of boiling water at 1 atm keeps rising as heat is supplied continuously. Reason (R): Heat is absorbed during a change of state.
1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is not the correct explanation of A
3. A is true but R is false
4. A is false but R is true
Answer
D. A is false but R is true
A is false: the temperature stays at 100 °C during boiling. R is true: the heat is the latent heat.
Assertion (A): A hotter body appears bluish and a cooler body appears reddish. Reason (R): The wavelength of maximum emission is inversely proportional to the absolute temperature.
1. Both A and R are true but R is not the correct explanation of A
2. A is true but R is false
3. Both A and R are true and R is the correct explanation of A
4. A is false but R is true
Answer
C. Both A and R are true and R is the correct explanation of A
By λm T = b, a higher T gives a shorter λm, so the colour shifts towards blue. R explains A.
Assertion (A): Gaps are left between iron rails. Reason (R): Iron has a high melting point.
1. Both A and R are true and R is the correct explanation of A
2. A is true but R is false
3. Both A and R are true but R is not the correct explanation of A
4. A is false but R is true
Answer
C. Both A and R are true but R is not the correct explanation of A
Gaps allow expansion on heating. The high melting point is true but does not explain the gaps.
Assertion (A): The water at the bottom of a deep lake in winter stays at about 4 °C. Reason (R): Water has maximum density at 4 °C.
1. Both A and R are true and R is the correct explanation of A
2. Both A and R are true but R is not the correct explanation of A
3. A is true but R is false
4. A is false but R is true
Answer
A. Both A and R are true and R is the correct explanation of A
The densest water at 4 °C sinks to the bottom, and ice forms at the top. R explains A.
Match List I with List II. List I: a. Specific heat capacity b. Latent heat c. Thermal conductivity d. Stefan's constant List II: i. W m⁻¹ K⁻¹ ii. J kg⁻¹ iii. J kg⁻¹ K⁻¹ iv. W m⁻² K⁻⁴
1. a-ii, b-iii, c-i, d-iv
2. a-iii, b-ii, c-iv, d-i
3. a-iii, b-i, c-ii, d-iv
4. a-iii, b-ii, c-i, d-iv
Answer
D. a-iii, b-ii, c-i, d-iv
Specific heat: J kg⁻¹ K⁻¹ (iii). Latent heat: J kg⁻¹ (ii). Conductivity: W m⁻¹ K⁻¹ (i). σ: W m⁻² K⁻⁴ (iv).
Match List I with List II. List I: a. Stefan-Boltzmann law b. Wien's law c. Newton's law of cooling d. Law of heat conduction List II: i. λm T = constant ii. Power radiated ∝ T⁴ iii. Rate of cooling ∝ excess temperature iv. Q/t = KAΔT/L
1. a-ii, b-i, c-iii, d-iv
2. a-i, b-ii, c-iii, d-iv
3. a-ii, b-i, c-iv, d-iii
4. a-ii, b-iii, c-i, d-iv
Answer
A. a-ii, b-i, c-iii, d-iv
a: power ∝ T⁴ (ii). b: λm T = constant (i). c: rate ∝ excess temperature (iii). d: Q/t = KAΔT/L (iv).
Match List I with List II. List I: a. Ice point b. Steam point c. Absolute zero d. Triple point of water List II: i. 273.16 K ii. 373.15 K iii. 0 K iv. 273.15 K
1. a-iv, b-iii, c-ii, d-i
2. a-iv, b-ii, c-i, d-iii
3. a-ii, b-iv, c-iii, d-i
4. a-iv, b-ii, c-iii, d-i
Answer
D. a-iv, b-ii, c-iii, d-i
Ice point 273.15 K (iv), steam point 373.15 K (ii), absolute zero 0 K (iii), triple point 273.16 K (i).
Match List I with List II. List I: a. Linear expansion b. Area expansion c. Volume expansion d. Heat absorbed in warming List II: i. ΔA = 2αAΔT ii. ΔV = 3αVΔT iii. Q = mcΔT iv. ΔL = αLΔT
1. a-i, b-iv, c-ii, d-iii
2. a-iv, b-i, c-iii, d-ii
3. a-iv, b-ii, c-i, d-iii
4. a-iv, b-i, c-ii, d-iii
Answer
D. a-iv, b-i, c-ii, d-iii
Linear: ΔL = αLΔT (iv). Area: ΔA = 2αAΔT (i). Volume: ΔV = 3αVΔT (ii). Heat: Q = mcΔT (iii).
Match List I with List II. List I: a. Latent heat of fusion of ice b. Latent heat of vaporisation of water c. Specific heat capacity of water d. Stefan's constant List II: i. 4186 J kg⁻¹ K⁻¹ ii. 3.33 × 10⁵ J kg⁻¹ iii. 2.26 × 10⁶ J kg⁻¹ iv. 5.67 × 10⁻⁸ W m⁻² K⁻⁴
1. a-ii, b-iii, c-i, d-iv
2. a-iii, b-ii, c-i, d-iv
3. a-ii, b-i, c-iii, d-iv
4. a-ii, b-iii, c-iv, d-i
Answer
A. a-ii, b-iii, c-i, d-iv
Fusion 3.33 × 10⁵ (ii); vaporisation 2.26 × 10⁶ (iii); c of water 4186 (i); σ 5.67 × 10⁻⁸ (iv).
Match List I with List II. List I: a. Water pipes burst in severe cold b. Sea breeze in the day c. Gaps in railway tracks d. Fish survive in a frozen lake List II: i. Land heats faster than the sea ii. Thermal expansion of metal iii. Water expands on freezing iv. Water at the bottom stays at 4 °C
1. a-iii, b-i, c-ii, d-iv
2. a-iii, b-i, c-iv, d-ii
3. a-iii, b-ii, c-i, d-iv
4. a-i, b-iii, c-ii, d-iv
Answer
A. a-iii, b-i, c-ii, d-iv
Pipes: water expands on freezing (iii). Sea breeze: land heats faster (i). Rails: thermal expansion (ii). Fish: water at 4 °C at the bottom (iv).
Two slabs of equal area are in contact. Slab A is 0.1 m thick with K = 200 W m⁻¹ K⁻¹; slab B is 0.2 m thick with K = 100 W m⁻¹ K⁻¹. The free face of A is at 100 °C and the free face of B is at 0 °C. In the steady state the temperature of the interface is
1. 20 °C
2. 50 °C
3. 80 °C
4. 67 °C
Answer
C. 80 °C
Resistances per unit area: A = 5 × 10⁻⁴, B = 2 × 10⁻³. Drop across A = 100 × 5 × 10⁻⁴/(2.5 × 10⁻³) = 20 °C, so the interface is at 80 °C.
A body cools from 80 °C to 60 °C in 10 minutes in surroundings at 30 °C. Assuming Newton's law of cooling, the time it takes to cool from 60 °C to 40 °C is
1. 15 minutes
2. 10 minutes
3. 30 minutes
4. 20 minutes
Answer
D. 20 minutes
20/10 = k(70 − 30) gives k = 0.05 per min. Then 20/t = 0.05 × (50 − 30) = 1, so t = 20 min.
Take σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. A blackbody of surface area 0.01 m² is at 1000 K. The power it radiates is
1. 5.67 W
2. 567 W
3. 5670 W
4. 56.7 W
Answer
B. 567 W
P = σAT⁴ = 5.67 × 10⁻⁸ × 0.01 × 10¹² = 567 W.
A blackbody at 500 K is placed in surroundings at 250 K. The ratio of the net power it loses to the power it emits is
1. 3/4
2. 15/16
3. 1/16
4. 7/8
Answer
B. 15/16
Net/emitted = (T⁴ − T₀⁴)/T⁴ = 1 − (1/2)⁴ = 15/16.
Star P has its peak emission at 450 nm and star Q at 1350 nm. Both radiate as blackbodies. The ratio T_P/T_Q is
1. 1/3
2. 9
3. 3
4. 81
Answer
C. 3
λm T = constant, so T_P/T_Q = λ_Q/λ_P = 1350/450 = 3.
In an insulated vessel, 10 g of steam at 100 °C is passed into 300 g of water at 20 °C. Take L of vaporisation = 540 cal g⁻¹ and c of water = 1 cal g⁻¹ °C⁻¹. The final temperature is
1. 30 °C
2. 35 °C
3. 50 °C
4. 40 °C
Answer
D. 40 °C
Heat released = 10 × 540 + 10 × (100 − T). Heat gained = 300 × (T − 20). 5400 + 1000 − 10T = 300T − 6000 gives 310T = 12 400 and T = 40 °C.
A strip made of brass (α = 19 × 10⁻⁶ K⁻¹) riveted to a strip of iron (α = 12 × 10⁻⁶ K⁻¹) is heated. The strip bends so that
1. brass is on the outer (convex) side
2. it stays straight
3. iron is on the outer (convex) side
4. brass is on the inner (concave) side and the strip becomes shorter
Answer
A. brass is on the outer (convex) side
Brass has the larger α, so it lengthens more and lies on the outside of the curve.

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1.The camel's hump is a store of-
2.The chemical composition of the ruby gemstone is:
3.The covalent bonding behaviour of the carbon compounds corresponds to which of the following characteristics of these compounds?
4.The conversion of liquid state into solid state is known as-
5.The basic modification with a “prefix” or “suffix” in the nomenclature is the indicator of:
6.The formula unit mass of a substance is the sum of the atomic masses of all atoms in a formula unit of a/an:
7.The gas usually filled in the electric bulb is
8.The gas released on the reaction of metal carbonate with hydrochloric acid turns lime water milky. The released gas is:
9.The DNA in the cell nucleus is the information source for the making of which of the following substances?
10.The drying of milk of lime (white washing) is due to the action of-

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