JEE Advanced 2014 · Paper 1 · Chemistry Q24

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ChemistryMultiple correct+3Question 24 of 60

An ideal gas in a thermally insulated vessel at internal pressure $=P_1$ , volume $=V_1$ and absolute temperature $=T_1$ expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are $P_2$ , $V_2$ and $T_2$ , respectively. For this expansion,

Two thermally insulated vessels. Left: gas (P₁, V₁, T₁) held below a piston with an evacuated space above (P_ext = 0). Arrow labelled Irreversible. Right: the piston has risen to the stops; the gas now occupies (P₂, V₂, T₂) with P_ext = 0 above.

q=0

T_2=T_1

P_2V_2=P_1V_1

P_2V_2^\gamma=P_1V_1^\gamma

Answer and worked solution

Official answer: A, B, C

Free expansion of an ideal gas.

(A) The vessel is thermally insulated, so $q=0$ . True.
(B) $P_\text{ext}=0$ , so $w=0$ ; then $\Delta U=0$ , and for an ideal gas $T_2=T_1$ . True.
(C) Since $T$ is unchanged, $P_2V_2=nRT_2=nRT_1=P_1V_1$ . True.
(D) $PV^\gamma=$ constant holds for a reversible adiabatic process, not for this irreversible one. False.

(A), (B), (C)

Topics:First law and enthalpy

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JEE Advanced 2014 · Paper 1, Chemistry question 24