Chemistry · Thermodynamics & Thermochemistry

JEE Advanced 2018 — Paper 1 — Question 18

A reversible cyclic process for an ideal gas is shown below. Here, $P, V$ , and $T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q, w, H$ and $U$ are heat, work, enthalpy and internal energy, respectively. The correct option(s) is (are)

Option A:
$\mathrm{q}_{\mathrm{AC}}=\Delta \mathrm{U}_{\mathrm{BC}}$ and $\mathrm{w}_{\mathrm{AB}}=\mathrm{P}_{2}\left(\mathrm{~V}_{2}-\mathrm{V}_{1}\right)$
Option B:
$\mathrm{w}_{\mathrm{BC}}=\mathrm{P}_{2}\left(\mathrm{~V}_{2}-\mathrm{V}_{1}\right)$ and $\mathrm{q}_{\mathrm{BC}}=\Delta \mathrm{H}_{\mathrm{AC}}$
Correct
Option C:
$\Delta \mathrm{H}_{\mathrm{CA}}<\Delta \mathrm{U}_{\mathrm{CA}}$ and $\mathrm{q}_{\mathrm{AC}}=\Delta \mathrm{U}_{\mathrm{BC}}$
Correct
Option D:
$\mathrm{q}_{\mathrm{BC}}=\Delta \mathrm{H}_{\mathrm{AC}}$ and $\Delta \mathrm{H}_{\mathrm{CA}}>\Delta \mathrm{U}_{\mathrm{CA}}$

Answer: B, C

Step-by-step solution

$\Delta \mathrm{H}_{\mathrm{AC}}+\Delta \mathrm{H}_{\mathrm{CB}}+\Delta \mathrm{H}_{\mathrm{BA}}=0$

$\Delta \mathrm{H}_{\mathrm{BA}}=0$ (Temperature is constant)

$\Delta \mathrm{H}_{\mathrm{AC}}=\Delta \mathrm{H}_{\mathrm{BC}} …(1)$

We know that $\mathrm{q}_{\mathrm{P}}=\Delta H$ (In path $B C, P=$ constant)

Hence $q_{B C}=\Delta H_{B C}$

From Eq. (1)

$\mathrm{q}_{\mathrm{BC}}=\Delta \mathrm{H}_{\mathrm{AC}}$

(B) $\mathrm{q}_{\mathrm{BC}}=-\mathrm{P}_{2}\left(\mathrm{~V}_{1}-\mathrm{V}_{2}\right)=\mathrm{P}_{2}\left(\mathrm{~V}_{2}-\mathrm{V}_{1}\right)$

(C) $\Delta \mathrm{H}_{\mathrm{CA}}=\mathrm{nC}_{\mathrm{P}}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)=-\mathrm{nC}_{\mathrm{P}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)$

$\Delta \mathrm{U}_{\mathrm{CA}}=\mathrm{nC}_{\mathrm{V}}\left(\mathrm{T}_{1}-\mathrm{T}_{2}\right)=-\mathrm{nC}_{\mathrm{V}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)$

As, $\mathrm{C}_{\mathrm{P}}>\mathrm{C}_{\mathrm{V}}$

So, $\Delta \mathrm{H}_{\mathrm{CA}}<\Delta \mathrm{U}_{\mathrm{CA}}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2018
Paper: Paper 1
Subject: Chemistry
Chapter: Thermodynamics & Thermochemistry
Topic: Internal Energy and the First Law