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Thermal equilibrium, zeroth law and temperature: NEET MCQs with answers

50 questions on this topic of Thermodynamics (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. Which of the following conditions must be satisfied simultaneously for two thermodynamic systems to be in complete thermodynamic equilibrium with one another?

  1. Thermal equilibrium only
  2. Thermal, mechanical, and chemical equilibrium
  3. Mechanical and chemical equilibrium only
  4. Thermal and radiative equilibrium only
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Answer: (B) Thermal, mechanical, and chemical equilibrium

Thermodynamic equilibrium requires that there is no net macroscopic change in the state of the systems. This entails mechanical equilibrium (balanced forces/pressures), chemical equilibrium (no net chemical reactions or diffusion), and thermal equilibrium (equal temperatures).

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2. A constant-volume gas thermometer using an ideal gas shows a pressure of 1.50 × 10⁵ Pa at the triple point of water (273.16 K). When immersed in a liquid bath, the pressure recorded is 2.25 × 10⁵ Pa. What is the absolute temperature of the bath?

  1. 409.74 K
  2. 182.11 K
  3. 364.21 K
  4. 450.00 K
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Answer: (A) 409.74 K

For a constant-volume ideal gas thermometer, T = 273.16 × (P / P_tr). Substituting the given values gives T = 273.16 × (2.25 × 10⁵ / 1.50 × 10⁵) = 273.16 × 1.5 = 409.74 K.

hard

3. Three bodies A, B, and C have equal heat capacities. Initially, body A is at 10 °C, body B is at 40 °C, and body C is at 70 °C. First, body A and body B are brought into thermal contact until thermal equilibrium is reached, and then separated. Next, body B is brought into thermal contact with body C until equilibrium is reached. Neglecting heat losses to the surroundings, the final temperature of body B is:

  1. 40.0 °C
  2. 52.5 °C
  3. 47.5 °C
  4. 55.0 °C
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Answer: (C) 47.5 °C

Since all three bodies have identical heat capacities C_h: When A (10 °C) and B (40 °C) attain equilibrium, their common temperature is T_AB = (10 + 40) / 2 = 25 °C. Next, body B (now at 25 °C) is placed in contact with C (at 70 °C). Their final equilibrium temperature is T_BC = (25 + 70) / 2 = 95 / 2 = 47.5 °C.

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4. A Celsius thermometer and a Fahrenheit thermometer are dipped into a liquid bath. If the reading on the Fahrenheit thermometer is numerically equal to three times the reading on the Celsius thermometer, what is the temperature of the liquid bath in degrees Celsius?

  1. 80.0 °C
  2. 26.7 °C
  3. 17.8 °C
  4. 40.0 °C
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Answer: (B) 26.7 °C

Using the relation F = (9/5)C + 32, we substitute F = 3C. This gives 3C = 1.8C + 32, which simplifies to 1.2C = 32. Therefore, C = 32 / 1.2 = 26.67 °C ≈ 26.7 °C.

easy

5. An insulating container is divided into two compartments by an impermeable fixed partition. Compartment 1 contains gas at pressure P₁ and volume V₁, while compartment 2 contains gas at pressure P₂ and volume V₂. The partition is diathermic. When steady state is reached, which physical quantity must definitely be identical in both compartments?

  1. The absolute temperature
  2. The internal energy density
  3. The product of pressure and volume (P × V)
  4. The ratio of specific heats (Cp/Cv)
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Answer: (A) The absolute temperature

A diathermic wall permits heat exchange but restricts mass transfer and mechanical expansion. Therefore, thermal equilibrium is established across the wall, ensuring that the temperatures of the gases in the two compartments become equal, while their pressures and volumes remain independent.

hard

6. Two identical rigid vessels contain the same ideal monoatomic gas. Vessel 1 has 1 mole of gas at 300 K, while Vessel 2 has 2 moles of gas at 600 K. The two vessels are connected through a thin diathermic valve with no loss of gas or heat to the surroundings. After the system reaches complete thermal and mechanical equilibrium, what is the final temperature of the mixture?

  1. 450 K
  2. 520 K
  3. 500 K
  4. 400 K
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Answer: (C) 500 K

Because the combined system is rigid and thermally isolated from the outside, the total internal energy is conserved: U_total = U₁ + U₂. For a monoatomic ideal gas, U = n(3/2)RT. Thus, (n₁ + n₂) (3/2) R T_f = n₁ (3/2) R T₁ + n₂ (3/2) R T₂. Cancelling (3/2)R gives T_f = (n₁ T₁ + n₂ T₂) / (n₁ + n₂) = (1 × 300 + 2 × 600) / (1 + 2) = 1500 / 3 = 500 K.

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7. Systems A and B are each separately in thermal equilibrium with system C. Then:

  1. Nothing can be said about A and B
  2. A and B are in thermal equilibrium with each other
  3. A is hotter than B
  4. B is hotter than A
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Answer: (B) A and B are in thermal equilibrium with each other

This is the zeroth law of thermodynamics: two systems each in thermal equilibrium with a third are in thermal equilibrium with each other.

NCERT Class 11

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8. A faulty mercury thermometer has its lower fixed point marked at -2 °C and its upper fixed point marked at 102 °C at normal atmospheric pressure. What is the true temperature in degrees Celsius when this faulty thermometer reads 50 °C?

  1. 50.0 °C
  2. 48.0 °C
  3. 52.0 °C
  4. 51.5 °C
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Answer: (A) 50.0 °C

Using the linear scale relation, (T - LFP)/(UFP - LFP) is constant. Here, (50 - (-2))/(102 - (-2)) = 52/104 = 0.5. Hence, the true temperature on the standard Celsius scale is 0.5 × 100 °C = 50.0 °C.

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9. In a constant-volume gas thermometer, the pressure of a given mass of gas is 80.0 cm of Hg at 0 °C and 109.3 cm of Hg at 100 °C. When the thermometer is inserted into an oil bath, the pressure reads 95.0 cm of Hg. What is the temperature of the oil bath?

  1. 51.2 °C
  2. 54.5 °C
  3. 48.3 °C
  4. 58.0 °C
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Answer: (A) 51.2 °C

Temperature on the constant-volume gas scale is given by T = [(P_T - P₀)/(P₁₀₀ - P₀)] × 100 °C. Substituting the given values: T = [(95.0 - 80.0)/(109.3 - 80.0)] × 100 = (15.0 / 29.3) × 100 ≈ 51.19 °C ≈ 51.2 °C.

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10. Statement I: Two bodies at the same temperature must contain equal amounts of internal thermal energy. Statement II: Temperature determines the direction of spontaneous flow of heat between two bodies placed in thermal contact.

  1. Both Statement I and Statement II are correct
  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 incorrect
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Answer: (C) Statement I is incorrect but Statement II is correct

Statement I is incorrect because internal energy depends on the mass, temperature, and specific heat capacity (or degrees of freedom) of the bodies, not just temperature. Statement II is correct because heat flows spontaneously from a body at higher temperature to one at lower temperature.

easy

11. Consider the following two statements regarding thermal equilibrium and the zeroth law of thermodynamics: Statement I: If system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A and system C are also in thermal equilibrium with each other. Statement II: The Zeroth Law of Thermodynamics establishes temperature as a valid physical property that determines whether two systems will be in thermal equilibrium. Choose the correct option:

  1. Both Statement I and Statement II are correct.
  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 incorrect.
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Answer: (A) Both Statement I and Statement II are correct.

Statement I is the formal assertion of the Zeroth Law of Thermodynamics. Statement II is also correct because the zeroth law ensures that all systems in mutual thermal equilibrium possess a common physical parameter, which is identified as temperature.

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12. At what temperature do the numerical values on the Fahrenheit scale and the Kelvin scale coincide?

  1. 313.25
  2. -40.00
  3. 574.25
  4. 233.15
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Answer: (C) 574.25

Let the common reading be x. The conversion formula is (x - 32)/180 = (x - 273.15)/100, which simplifies to (x - 32)/9 = (x - 273.15)/5. Solving gives 5x - 160 = 9x - 2458.35, leading to 4x = 2298.35, or x ≈ 574.25.

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