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  • A sample of gas with is taken through an adiabatic process in which the volume is compressed from <img alt="1200 \mathrm{~cm}^{3}$ to $300 \mathrm{~cm}^{3}" src="h

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 \mathrm{kPa}. The absolute value of the workdone by the gas in the process =____________J.

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best_answer

V_{f}= 300cm^{3}=300\times10^{-6}m^{3}\\

V_{i}=1200cm^{3}=1200\times10^{-6}m^{3}\\

P_{i}=200KPa=200\times10^{3}Pa\\

For adiabatic process

P_{i}V_{i}^{\gamma }=P_{f}V_{f}^{\gamma }\\

\gamma =1.5=\frac{3}{2}\\

\left ( 200\times10^{3} \right )\times\left ( 1200 \right )^{3/2}=P_{f}\left ( 300 \right )^{3/2}\\

1600\times10^{3}P_{f}\\

W=\frac{P_{f}V_{f}-P_{i}V_{i}}{\gamma -1}=\frac{480-240}{1/2}=480J

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vishal kumar

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