A vessel contains $0.15 \mathrm{~m}^{3}$ of a gas at pressure 8 bar and temperature $140^{\circ} \mathrm{C}$ with $\mathrm{c}_{\mathrm{p}}=3 \mathrm{R}$ and $\mathrm{c}_{\mathrm{v}}=2 \mathrm{R}$. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ____ kJ. (R is gas constant)

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Heat & Thermodynamics

A vessel contains

0.15 m^{3}

of a gas at pressure 8 bar and temperature

14 0^{\circ} C

with

c_{p} = 3 R

and

c_{v} = 2 R

. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ____ kJ. (R is gas constant)

Answer: 120

Solution

The ratio of specific heats is

γ = \frac{c _{p}}{c _{v}} = \frac{3 R}{2 R} = 1.5

. For the adiabatic expansion

P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}

, so

V_{2} = V_{1} (P_{1} / P_{2})^{1/ γ} = 0.15 \times 8^{2/3} = 0.15 \times 4 = 0.6 m^{3}

. The work done is

W = \frac{P _{1} V _{1} - P _{2} V _{2}}{γ - 1} = \frac{( 8 \times 1 0 ^{5} ) ( 0.15 ) - ( 1 \times 1 0 ^{5} ) ( 0.6 )}{0.5} = \frac{0.6 \times 1 0 ^{5}}{0.5} = 1.2 \times 1 0^{5} J

. The work done during the process is

120

kJ.

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Heat & Thermodynamics →

More JEE Main questions on Heat & Thermodynamics

A cylindrical tube $A B$ of length $l$ , closed at both ends contains an ideal gas of 1 mol having molecular weight $M$ . The tube is rotated in a horizontal plane with constant angular velocity $ω$ about an axis perpendicular to $A B$ and passing through the edge at end A, as s …
JEE Main 2026View solution →
Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $10 0^{\circ} C$ and $4 0^{\circ} C$ respectively. Given the thermal conductivity of rod x is three …
JEE Main 2026View solution →
The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{th}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $Δ Q = 0$ ) then identify the gas from the following options (Assuming …
JEE Main 2026View solution →
Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is …
JEE Main 2026View solution →
An insulated cylinder of volume $60 cm^{3}$ is filled with a gas at $2 7^{\circ} C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 cm^{3}$ while allowing the temperature to rise to $7 7^{\circ} C$ . The fin …
JEE Main 2026View solution →
The r.m.s speed of oxygen molecules at $4 7^{\circ} C$ is equal to that of the hydrogen molecules kept at $____$ $^{\circ} C$ . (Mass of oxygen molecule/mass of hydrogen molecule=32/2)
JEE Main 2026View solution →