JEE Advanced 2017 · Paper 1 · Physics Q16

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PhysicsSingle correct+3 / -1Question 16 of 54

Passage

Answer Q.16, Q.17 and Q.18 by appropriately matching the information given in the three columns of the following table.

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V$ diagrams in column 3 of the table. Consider only the path from state 1 to state 2. $W$ denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here $\gamma$ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is $n$ .

Column 1	Column 2	Column 3
(I) $W_{1\to2} = \frac{1}{\gamma - 1}(P_2V_2 - P_1V_1)$	(i) Isothermal	(P) [P-V plot]
(II) $W_{1\to2} = -PV_2 + PV_1$	(ii) Isochoric	(Q) [P-V plot]
(III) $W_{1\to2} = 0$	(iii) Isobaric	(R) [P-V plot]
(IV) $W_{1\to2} = -nRT\ln\left(\frac{V_2}{V_1}\right)$	(iv) Adiabatic	(S) [P-V plot]

The three-column table for Q.16-18. Column 3 holds four P-V diagrams of a cycle, each highlighting the path from state 1 to state 2: (P) a horizontal arrow at the top of the cycle from 1 to 2 (constant pressure, expansion); (Q) a falling curve from 1 down to 2 along the lower-right side of the cycle (expansion along a curve); (R) a gently falling curve from 1 at the top left to 2 along the top of the cycle (expansion along a curve); (S) a vertical segment between 1 (above) and 2 (below) on the left side of the cycle, at constant volume.

Which of the following options is the only correct representation of a process in which $\Delta U = \Delta Q - P\Delta V$ ?

(II) (iv) (R)

(III) (iii) (P)

(II) (iii) (S)

(II) (iii) (P)

Answer and worked solution

Official answer: D

$\Delta U=\Delta Q-P\Delta V$ with a single constant pressure $P$ describes an isobaric process (iii).

The work done on the gas is then $W=-P(V_2-V_1)=-PV_2+PV_1$ , which is (II).

The isobaric $P$ - $V$ path is the horizontal step (P).

(D)

Topics:Thermodynamic processes First law and internal energy Work done by a gas

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JEE Advanced 2017 · Paper 1, Physics question 16