A vessel contains of a gas at pressure 8 bar and temperature with and . It is expanded adiabatically till pressure

Question

A vessel contains $0.15 m^{3}$ of a gas at pressure 8 bar and temperature $140 ° C$ 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) [2026]

Smart Achievers · Accepted Answer

(120)

$γ = \frac{C_{p}}{C_{v}} = \frac{3}{2}$

$∵$ $P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ} \Rightarrow V_{2} = {(\frac{P_{1}}{P_{2}})}^{1 / γ} V_{1}$

$\Rightarrow V_{2} = {(\frac{8}{1})}^{2 / 3} \times 0.15 = 0.6 m^{3}$

$Work done in adiabatic process, W = \frac{P_{1} V_{1} - P_{2} V_{2}}{γ - 1}$

$W = (\frac{8 \times 0.15 - 1 \times 0.6}{1.5 - 1}) \times 10^{5} = 1.2 \times 10^{5} J$

$\Rightarrow W = 120 kJ$

Solution

Q.
A vessel contains $0.15 m^{3}$ of a gas at pressure 8 bar and temperature $140 ° C$ 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) [2026]

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Solution

Q. A vessel contains 0.15 m3 of a gas at pressure 8 bar and temperature 140°C with Cp=3R and Cv=2R. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is ________ kJ. (R is gas constant) [2026]

Ans. (120) γ=CpCv=32 ∵ P1V1γ=P2V2γ⇒V2=(P1P2)1/γV1 ⇒V2=(81)2/3×0.15=0.6 m3 Work done in adiabatic process, W=P1V1-P2V2γ-1 W=(8×0.15-1×0.61.5-1)×105=1.2×105 J ⇒W=120 kJ

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Q.
A vessel contains $0.15 m^{3}$ of a gas at pressure 8 bar and temperature $140 ° C$ 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) [2026]