JEE Advanced 2019 · Paper 2 · Physics Q18

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PhysicsList match+3 / -1Question 18 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 on one mole of monatomic ideal gas is as shown in the $TV$ -diagram with $P_0V_0 = \frac13RT_0$ , the correct match is,

T-V diagram: 1 (V₀, T₀/3) → 2 (2V₀, T₀/3) at constant temperature, then 2 → 3 (2V₀, T₀) 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 → P, II → R, III → T, IV → S

I → P, II → T, III → Q, IV → T

I → P, II → R, III → T, IV → P

I → S, II → T, III → Q, IV → U

Answer and worked solution

Official answer: C

The process. $1\to2$ is isothermal at $\frac{T_0}3$ from $V_0$ to $2V_0$ ; $2\to3$ is isochoric, heating the gas to $T_0$ .

The quantities.

I. Work. Only the isothermal step does work: $R\frac{T_0}3\ln2$ , (P).
II. Change in internal energy. $\frac32R\cdot\frac{2T_0}3=RT_0$ , (R).
III. Heat over $1\to2\to3$ . $\frac13RT_0\ln2+RT_0=\frac13RT_0(3+\ln2)$ , (T).
IV. Heat in $1\to2$ . For an isothermal step it equals the work, $\frac13RT_0\ln2$ , (P).

(C)

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

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JEE Advanced 2019 · Paper 2, Physics question 18