JEE Advanced 2017 · Paper 1 · Chemistry Q1

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ChemistryMultiple correct+4 / -2Question 19 of 54

An ideal gas is expanded from $(\mathrm{p_1, V_1, T_1})$ to $(\mathrm{p_2, V_2, T_2})$ under different conditions. The correct statement(s) among the following is(are)

The work done on the gas is maximum when it is compressed irreversibly from

(\mathrm{p_2, V_2})

(\mathrm{p_1, V_1})

against constant pressure

\mathrm{p_1}

If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic

The work done by the gas is less when it is expanded reversibly from

\mathrm{V_1}

\mathrm{V_2}

under adiabatic conditions as compared to that when expanded reversibly from

\mathrm{V_1}

\mathrm{V_2}

under isothermal conditions

The change in internal energy of the gas is (i) zero, if it is expanded reversibly with

\mathrm{T_1 = T_2}

, and (ii) positive, if it is expanded reversibly under adiabatic conditions with

\mathrm{T_1 \ne T_2}

Answer and worked solution

Official answer: A, B, C

(A) Compressing irreversibly against the constant pressure $p_1$ (the highest pressure on the path) gives work $p_1(V_2-V_1)$ . That is more than any other path from $(p_2,V_2)$ to $(p_1,V_1)$ . True.
(B) In a free expansion $w=0$ , and if it is fast $q=0$ . Then $\Delta U=0$ , so $T$ stays constant for an ideal gas. The process is both adiabatic and isothermal. True.
(C) Between the same volumes, the reversible adiabatic curve lies below the isotherm. Less area means less work by the gas. True.
(D) Part (i) is right, but in a reversible adiabatic expansion the gas does work at the expense of $U$ . So $\Delta U<0$ , not positive. False.

(A), (B), (C)

Topics:First law and enthalpy Entropy

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JEE Advanced 2017 · Paper 1, Chemistry question 1