JEE Advanced 2026 · Paper 1 · Physics Q7

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PhysicsMultiple correct+4 / -1Question 23 of 48

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process ( $\boldsymbol{ab}$ ), followed by an isochoric process ( $\boldsymbol{bc}$ ) and an adiabatic process ( $\boldsymbol{ca}$ ) as shown in the figure. The volumes of the gas are $V_1$ and $V_2$ at $\boldsymbol a$ and $\boldsymbol b$ , respectively. If the cycle has heat input $Q_{\text{in}}$ and output $Q_{\text{out}}$ , then the efficiency of the cycle is defined as $\eta=\dfrac{Q_{\text{in}}-Q_{\text{out}}}{Q_{\text{in}}}$ . The correct statement(s) is/are:
[Given: $\ln2\approx0.7$ ]

P-V diagram: from a (at V₁) an isothermal curve runs to b (at V₂); bc drops vertically at V₂ to c; the steeper adiabat ca returns to a. Arrows show the cycle a → b → c → a.

V_2/V_1=8

, the heat released in the process

\boldsymbol{bc}

is smaller than the heat absorbed in the process

\boldsymbol{ab}

For a given value of

V_2/V_1

\eta

does not depend on the temperature of the isothermal process.

V_2/V_1=8

, then the temperature of the gas at

\boldsymbol a

is 4 times the temperature of the gas at

\boldsymbol c

V_2/V_1=8

, then the pressure of the gas at

\boldsymbol a

is 4 times the pressure of the gas at

\boldsymbol b

Answer and worked solution

Official answer: A, B, C

Monoatomic gas, $\gamma=\frac53$ . Let $T_h$ be the isotherm temperature and $r=V_2/V_1$ .

Temperatures. The adiabat $ca$ joins $V_2$ to $V_1$ : $T_cV_2^{2/3}=T_hV_1^{2/3}$ , so $\dfrac{T_h}{T_c}=r^{2/3}$ . For $r=8$ this is $4$ . (C) true.

Heats (per mole).

Absorbed on $ab$ : $Q_{ab}=RT_h\ln r$ .
Released on $bc$ : $Q_{bc}=\frac32R(T_h-T_c)=\frac32RT_h\left(1-r^{-2/3}\right)$ .

(A) For $r=8$ : $Q_{ab}=3(0.7)RT_h=2.1RT_h$ and $Q_{bc}=\frac98RT_h\approx1.13RT_h$ . Released < absorbed. True.

(B) $\eta=1-\dfrac{\frac32\left(1-r^{-2/3}\right)}{\ln r}$ depends only on $r$ . True.

(D) On the isotherm $P_aV_1=P_bV_2$ , so $P_a/P_b=8$ , not 4. False.

Topics:Heat engines and refrigerators Thermodynamic processes

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