JEE Advanced 2019 · Paper 2 · Physics Q17

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PhysicsList match+3 / -1Question 17 of 54

Passage

Answer Q.17 and Q.18 by appropriately matching the lists based on the information given in the paragraph

In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by $T\Delta X$ , where $T$ is temperature of the system and $\Delta X$ is the infinitesimal change in a thermodynamic quantity $X$ of the system. For a mole of monatomic ideal gas $X = \frac32R\ln\left(\frac T{T_A}\right) + R\ln\left(\frac V{V_A}\right)$ . Here, $R$ is gas constant, $V$ is volume of gas, $T_A$ and $V_A$ are constants.

The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.

If the process carried out on one mole of monatomic ideal gas is as shown in figure in the $PV$ -diagram with $P_0V_0 = \frac13RT_0$ , the correct match is,

P-V diagram: 1 (V₀, P₀) → 2 (2V₀, P₀) at constant pressure, then 2 → 3 (2V₀, 3P₀/2) at constant volume.

List-I

I
Work done by the system in process $1\to2\to3$
II
Change in internal energy in process $1\to2\to3$
III
Heat absorbed by the system in process $1\to2\to3$
IV
Heat absorbed by the system in process $1\to2$

List-II

P
$\frac13RT_0\ln2$
Q
$\frac13RT_0$
R
$RT_0$
S
$\frac43RT_0$
T
$\frac13RT_0(3 + \ln2)$
U
$\frac56RT_0$

I → Q, II → R, III → P, IV → U

I → Q, II → R, III → S, IV → U

I → S, II → R, III → Q, IV → T

I → Q, II → S, III → R, IV → U

Answer and worked solution

Official answer: B

Here $dQ=T\,dX$ , so $X$ is the entropy. The answers need only the first law.

States, with $T=PV/R$ and $P_0V_0=\frac13RT_0$ :

state 1: $T_1=\frac{T_0}3$ ;
state 2: $T_2=\frac{2T_0}3$ ;
state 3: $T_3=T_0$ .

The quantities.

I. Work. Only the isobaric step $1\to2$ does work: $P_0V_0=\frac13RT_0$ , (Q).
II. Change in internal energy. $\frac32R\left(T_0-\frac{T_0}3\right)=RT_0$ , (R).
III. Heat over $1\to2\to3$ . $Q=W+\Delta U=\frac43RT_0$ , (S).
IV. Heat in $1\to2$ . $\frac52R\cdot\frac{T_0}3=\frac56RT_0$ , (U).

(B)

Topics:Thermodynamic processes First law and internal energy Second law and entropy

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JEE Advanced 2019 · Paper 2, Physics question 17