JEE Main 2026 — Physics Thermodynamics

2026integermedium

A vessel contains $0.15$ m $^3$ of a gas at pressure $8$ bar and temperature $140°$ C with $c_p = 3R$ and $c_v = 2R$ . It is expanded adiabatically till pressure falls to $1$ bar. The work done during this process is _______ kJ. ( $R$ is gas constant)

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Held on 2 Apr 2026 · Verified 6 Jul 2026.

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Solution

Given $P_1 = 8$ bar $= 8 \times 10^5$ Pa, $V_1 = 0.15$ m $^3$ , and $P_2 = 1$ bar $= 10^5$ Pa.

The adiabatic index $\gamma$ is given by:

$\gamma = \dfrac{c_p}{c_v} = \dfrac{3R}{2R} = 1.5$

For an adiabatic process, $P_1 V_1^\gamma = P_2 V_2^\gamma$ .

$V_2 = V_1 \left( \dfrac{P_1}{P_2} \right)^{\dfrac{1}{\gamma}}$

$V_2 = 0.15 \times \left( \dfrac{8}{1} \right)^{\dfrac{1}{1.5}} = 0.15 \times 8^{\dfrac{2}{3}} = 0.15 \times 4 = 0.6$ m $^3$

The work done during the adiabatic expansion is:

$W = \dfrac{P_1 V_1 - P_2 V_2}{\gamma - 1}$

$W = \dfrac{8 \times 10^5 \times 0.15 - 1 \times 10^5 \times 0.6}{1.5 - 1}$

$W = \dfrac{1.2 \times 10^5 - 0.6 \times 10^5}{0.5}$

$W = \dfrac{0.6 \times 10^5}{0.5} = 1.2 \times 10^5$ J

$W = 120$ kJ

Answer: $120$

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Solution

Given $P_1 = 8$ bar $= 8 \times 10^5$ Pa, $V_1 = 0.15$ m $^3$ , and $P_2 = 1$ bar $= 10^5$ Pa.

The adiabatic index $\gamma$ is given by:

$\gamma = \dfrac{c_p}{c_v} = \dfrac{3R}{2R} = 1.5$

For an adiabatic process, $P_1 V_1^\gamma = P_2 V_2^\gamma$ .

$V_2 = V_1 \left( \dfrac{P_1}{P_2} \right)^{\dfrac{1}{\gamma}}$

$V_2 = 0.15 \times \left( \dfrac{8}{1} \right)^{\dfrac{1}{1.5}} = 0.15 \times 8^{\dfrac{2}{3}} = 0.15 \times 4 = 0.6$ m $^3$

The work done during the adiabatic expansion is:

$W = \dfrac{P_1 V_1 - P_2 V_2}{\gamma - 1}$

$W = \dfrac{8 \times 10^5 \times 0.15 - 1 \times 10^5 \times 0.6}{1.5 - 1}$

$W = \dfrac{1.2 \times 10^5 - 0.6 \times 10^5}{0.5}$

$W = \dfrac{0.6 \times 10^5}{0.5} = 1.2 \times 10^5$ J

$W = 120$ kJ

Answer: $120$

JEE Main 2026 — Physics Thermodynamics

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JEE Main 2026 — Physics Thermodynamics

Did you get this right?

Solution

Your note

JEE Main Thermodynamics in other years

More JEE Main Thermodynamics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Waves & Oscillations

Keep practicing Thermodynamics