JEE Advanced 2019 Paper 1 · Chemistry · Chemical Thermodynamics · hard

One mole of an ideal monatomic gas (CV=3/2R, R=8.314 J mol^-1K^-1) at 300 K doubles its volume by three different routes: (i) reversible isothermal…

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One mole of an ideal monatomic gas (

C_V=\tfrac32R

R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}

) at

300\ \mathrm{K}

doubles its volume by three different routes: (i) reversible isothermal, (ii) reversible adiabatic, (iii) adiabatic free expansion into an evacuated rigid container so that the final volume is twice the initial. Choose the correct statement(s).

A. In (i), $\Delta S_{\text{system}}=R\ln2\approx5.76\ \mathrm{J\,K^{-1}}$ and $\Delta S_{\text{universe}}=0$ .
B. In (ii), $\Delta S_{\text{system}}=0$ and the final temperature is about $189\ \mathrm{K}$ .
C. In (iii), $\Delta S_{\text{system}}=0$ because $q=0$ .
D. The work done by the gas in (ii) is greater than that in (i).

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Answer: A, B

(i) Isothermal reversible:

\Delta S_{sys}=R\ln(V_2/V_1)=8.314\times0.693=5.76\ \mathrm{J\,K^{-1}}

and the surroundings lose the same entropy, so

\Delta S_{univ}=0

; (A) is true. (ii) Reversible adiabatic:

q_{rev}=0

\Delta S=0

, and

TV^{\gamma-1}

is constant with

\gamma-1=2/3

, giving

T_2=300(1/2)^{2/3}=189.0\ \mathrm{K}

; (B) is true. (iii) Free expansion has

q=0

but is irreversible; entropy is a state function and the end states equal those of (i) (ideal gas,

\Delta T=0

), so

\Delta S_{sys}=R\ln2>0

and (C) is false. Work: (i)

|w|=RT\ln2=1729\ \mathrm{J}

; (ii)

|w|=C_V\Delta T=1.5\times8.314\times111.0=1384\ \mathrm{J}

, which is smaller, so (D) is false.

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