A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $1200 \mathrm{~cm}^{3}$ to $300 \mathrm{~cm}^{3}$. If the initial pressure is 200 kPa. The absolute value of the work done by the gas in the process = $\_\_\_\_$ J.

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Heat & Thermodynamics

A sample of gas with

γ = 1.5

is taken through an adiabatic process in which the volume is compressed from

1200 cm^{3}

300 cm^{3}

. If the initial pressure is 200 kPa. The absolute value of the work done by the gas in the process =

____

Answer: 480

Solution

For the adiabatic compression

P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}

with

γ = 1.5

and

V_{1} / V_{2} = 4

P_{2} = P_{1} (\frac{V _{1}}{V _{2}})^{γ} = 200 \times 4^{1.5} = 200 \times 8 = 1600 kPa .

The work done by the gas is

W = \frac{P _{1} V _{1} - P _{2} V _{2}}{γ - 1} = \frac{( 2 \times 1 0 ^{5} ) ( 1.2 \times 1 0 ^{- 3} ) - ( 16 \times 1 0 ^{5} ) ( 3 \times 1 0 ^{- 4} )}{0.5} = \frac{240 - 480}{0.5} = - 480 J .

The absolute value of the work done by the gas is

480

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Integer answer

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