JEE Advanced · 2017 · 21 May 2017 · Paper 1 · Chemical Thermodynamics

An ideal gas is expanded from

(p_{1}, V_{1}, T_{1})

(p_{2}, V_{2}, T_{2})

under different conditions. The correct statement(s) among the following is(are)

(A)The work done on the gas is maximum when it is compressed irreversibly from $(p_{2}, V_{2})$ to $(p_{1}, V_{1})$ against constant pressure $p_{1}$ ✓ Correct
(B)If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic✓ Correct
(C)The work done by the gas is less when it is expanded reversibly from $V_{1}$ to $V_{2}$ under adiabatic conditions as compared to that when expanded reversibly from $V_{1}$ to $V_{2}$ under isothermal conditions✓ Correct
(D)The change in internal energy of the gas is (i) zero, if it is expanded reversibly with $T_{1} = T_{2}$ , and (ii) positive, if it is expanded reversibly under adiabatic conditions with $T_{1} \neq = T_{2}$

Answer: (A), (B), (C)

Solution

Option A: In irreversible compression against constant external pressure

p_{1}

, the work done on the gas is

w = p_{1} (V_{1} - V_{2})

, which is maximum for a given volume change.

Option B: In free expansion,

w = 0

(no external pressure) and

q = 0

(no heat exchange with surroundings), so

Δ U = 0

(isothermal) and

q = 0

(adiabatic).

Option C: For reversible adiabatic expansion, temperature decreases, so less work is done compared to isothermal expansion at constant temperature.

Option D: This is incorrect. For reversible adiabatic expansion with

T_{1} \neq = T_{2}

, temperature decreases (

T_{2} < T_{1}

), so

Δ U < 0

(negative), not positive.

Correct answers: A, B, C

JEE Advanced · 2017 · 21 May 2017 · Paper 1 · One or more correct options

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JEE Advanced · 2017 · 21 May 2017 · Paper 1 · Chemical Thermodynamics

Solution

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