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Isothermal and adiabatic processes: 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. An ideal gas at pressure P₀ is compressed to half its initial volume isothermally. The final pressure of the gas will be:

  1. P₀ / 2
  2. 2 P₀
  3. P₀
  4. 4 P₀
Show answer and explanation

Answer: (B) 2 P₀

According to Boyle's law for an isothermal process, P₁V₁ = P₂V₂. Here, P₀V₀ = P₂(V₀/2), which gives P₂ = 2P₀.

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2. Given below are two statements: Statement I: In an adiabatic expansion of an ideal gas, the temperature of the gas always decreases. Statement II: In an isothermal compression of an ideal gas, heat is released by the gas to the surroundings. In the light of the above statements, choose the most appropriate answer from the options given below:

  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
Show answer and explanation

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

In an adiabatic expansion, the gas does positive work (W > 0) with Q = 0, meaning ΔU = -W < 0, so the internal energy and temperature decrease (Statement I is correct). In an isothermal compression, work is done on the gas (W < 0) while ΔU = 0, leading to Q = W < 0, meaning heat is rejected to the surroundings (Statement II is correct).

hard

3. An ideal gas is taken through two separate processes starting from the same initial state (P₁, V₁): Process A: Isothermal compression to volume V₁ / 2. Process B: Adiabatic compression to volume V₁ / 2. If W_A and W_B represent the work done ON the gas in process A and process B respectively, then:

  1. W_A > W_B
  2. W_A = W_B
  3. W_B = W_A / γ
  4. W_B > W_A
Show answer and explanation

Answer: (D) W_B > W_A

During compression from V₁ to V₁ / 2, the adiabatic curve lies entirely above the isothermal curve on a P-V diagram. Since work done on the gas equals the area under the P-V curve, the adiabatic path requires a larger area under the curve, meaning W_B > W_A.

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4. One mole of an ideal gas (γ = 1.4) expands adiabatically such that its temperature falls from 400 K to 300 K. The work done by the gas is (Take R = 8.3 J/(mol·K)):

  1. 1550 J
  2. 2075 J
  3. 1037.5 J
  4. 4150 J
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Answer: (B) 2075 J

Work done in an adiabatic process is W = nR(T₁ - T₂) / (γ - 1). Substituting n = 1, R = 8.3 J/(mol·K), T₁ - T₂ = 100 K, and γ - 1 = 0.4: W = (1 × 8.3 × 100) / 0.4 = 830 / 0.4 = 2075 J.

easy

5. An ideal gas at initial pressure P is compressed adiabatically to one-eighth of its original volume. If the ratio of specific heats is γ = 5/3, the final pressure of the gas will be:

  1. 8P
  2. 32P
  3. 16P
  4. 64P
Show answer and explanation

Answer: (B) 32P

For an adiabatic process, PV^γ = constant. Therefore, P₂ = P₁(V₁/V₂)^γ = P(8)^(5/3) = P(2³)^(5/3) = P(2⁵) = 32P.

hard

6. An ideal gas at 300 K is expanded isothermally to twice its volume, performing work W_iso. The gas is then restored to its initial volume at the same temperature. Next, it is compressed adiabatically from V to V/2, requiring work W_adia. The ratio of the magnitude of work done |W_adia| to |W_iso| for a gas with γ = 1.5 is:

  1. (2 - √2) / ln 2
  2. (√2 - 1) / (2 ln 2)
  3. 2(√2 - 1) / ln 2
  4. ln 2 / (2(√2 - 1))
Show answer and explanation

Answer: (C) 2(√2 - 1) / ln 2

For isothermal expansion, |W_iso| = nRT ln 2. For adiabatic compression from V to V/2, T₂ = T(2)^(γ-1) = 300(2)^(0.5) = 300√2. The work done is |W_adia| = nR(T₂ - T) / (γ - 1) = nR(300)(√2 - 1) / 0.5 = 2nRT(√2 - 1). Therefore, the ratio |W_adia| / |W_iso| = 2(√2 - 1) / ln 2.

medium

7. Consider the following statements: Statement I: Sudden bursting of an automobile tyre is an adiabatic process accompanied by cooling of the air. Statement II: In an adiabatic expansion of an ideal gas, the gas does work at the expense of its own internal energy. 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
Show answer and explanation

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

Sudden bursting occurs too rapidly for any heat exchange with the surroundings (ΔQ = 0), making it an adiabatic expansion. Since W > 0 and ΔU = -W, internal energy decreases, causing the temperature to drop (cooling). Thus, both statements are correct.

easy

8. The bulk modulus of elasticity of an ideal gas of pressure P undergoing an isothermal process is E_iso, and undergoing an adiabatic process is E_adia. The ratio E_adia / E_iso is:

  1. 1
  2. γ - 1
  3. 1/γ
  4. γ
Show answer and explanation

Answer: (D) γ

Isothermal bulk modulus is given by E_iso = -V(dP/dV) = P. Adiabatic bulk modulus is given by E_adia = -V(dP/dV) = γP. Therefore, the ratio E_adia / E_iso = γ.

easy

9. The ratio of the slope of an adiabatic curve to that of an isothermal curve at any point on a P-V indicator diagram for an ideal gas is equal to:

  1. γ
  2. γ - 1
  3. 1 / γ
  4. γ + 1
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Answer: (A) γ

The slope of an isothermal curve is (dP/dV)_iso = -P/V, while the slope of an adiabatic curve is (dP/dV)_adia = -γ(P/V). Taking the ratio, (dP/dV)_adia / (dP/dV)_iso = γ.

easy

10. An ideal gas with adiabatic index γ is compressed adiabatically from volume V to V/n. The ratio of the final pressure to the initial pressure is:

  1. n
  2. n^(1 - γ)
  3. n^(γ - 1)
  4. n^γ
Show answer and explanation

Answer: (D) n^γ

For a reversible adiabatic process, P₁V₁^γ = P₂V₂^γ. Given V₁ = V and V₂ = V/n, we have P₂/P₁ = (V₁/V₂)^γ = (V / (V/n))^γ = n^γ.

medium

11. Consider the following statements regarding isothermal and adiabatic expansions of an ideal gas from the same initial state (P₀, V₀) to the same final volume V_f (where V_f > V₀): Statement I: The work done in isothermal expansion is greater than the work done in adiabatic expansion. Statement II: The final temperature in adiabatic expansion is lower than the initial temperature. 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.
Show answer and explanation

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

In a P-V diagram, the isothermal expansion curve lies above the adiabatic expansion curve because the adiabatic slope is steeper. Hence, the area under the isothermal curve is larger, so W_iso > W_adia (Statement I is correct). In adiabatic expansion, work is done at the expense of internal energy, so temperature decreases (Statement II is correct).

easy

12. During an isothermal expansion of an ideal gas, which of the following statements is correct regarding its internal energy (U) and the heat supplied (Q)?

  1. ΔU > 0 and Q = 0
  2. ΔU = 0 and Q = 0
  3. ΔU < 0 and Q = -W
  4. ΔU = 0 and Q = W
Show answer and explanation

Answer: (D) ΔU = 0 and Q = W

For an ideal gas, internal energy depends solely on temperature. In an isothermal process, the temperature remains constant, so ΔU = 0. According to the first law of thermodynamics, ΔQ = ΔU + W, which gives Q = W.

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