JEE Advanced 2022 · Paper 2 · Physics Q14

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PhysicsMultiple correct+4 / -2Question 32 of 54

In the given $P$ - $V$ diagram, a monoatomic gas $\left(\gamma = \frac53\right)$ is first compressed adiabatically from state $A$ to state $B$ . Then it expands isothermally from state $B$ to state $C$ . [Given: $\left(\frac13\right)^{0.6} \simeq 0.5$ , $\ln 2 \simeq 0.7$ ].

Which of the following statement(s) is(are) correct?

P-V diagram: pressure P (kPa) on the vertical axis, volume V (m^3) on the horizontal axis. State A is at V = 0.80 m^3, P = 100 kPa. An adiabatic compression curve (arrow) runs from A up and to the left to state B at P = 300 kPa (dashed horizontal line at 300 kPa; B's volume is not marked). From B an isothermal expansion curve (arrow) runs up and to the right to state C, which lies directly above A on the vertical line V = 0.80 m^3. Dashed guide lines mark P = 100 and P = 300 kPa.

The magnitude of the total work done in the process

A \to B \to C

is 144 kJ.

The magnitude of the work done in the process

B \to C

is 84 kJ.

The magnitude of the work done in the process

A \to B

is 60 kJ.

The magnitude of the work done in the process

C \to A

is zero.

Answer and worked solution

Official answer: Dropped: full marks to everyone

This question was dropped (marks to all) in the official key. Below is the standard working.

States.

$A$ : $(0.8\ \mathrm{m^3},\ 100$ kPa).
Adiabatic to 300 kPa: $V_B=0.8\left(\frac13\right)^{1/\gamma}=0.8(0.5)=0.4\ \mathrm{m^3}$ , so $P_BV_B=120$ kJ.
Isothermal to $V_C=0.8\ \mathrm{m^3}$ .

Work in each process.

$A\to B$ : $|W|=\dfrac{P_BV_B-P_AV_A}{\gamma-1}=\dfrac{120-80}{2/3}=60$ kJ, done on the gas. (C) is true.
$B\to C$ : $|W|=P_BV_B\ln\dfrac{V_C}{V_B}=120\ln2=84$ kJ, done by the gas. (B) is true.
$C\to A$ : the volume is constant, so $W=0$ . (D) is true.

Option (A). The net work for $A\to B\to C$ is $84-60=24$ kJ. Adding the magnitudes gives $60+84=144$ kJ. Read literally, (A) is false, but "magnitude of the total work" can be read either way, which is probably why the question was dropped.

Topics:Work done by a gas Thermodynamic processes

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JEE Advanced 2022 · Paper 2, Physics question 14