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Work Done on Compression of Gas

A cylinder contains \(16g\) of \(O_2\). The work done when the gas is compressed to \(75\%\) of the original volume at constant temperature of \(27^\circ\) is ________.

Discussion:

Given mass of \(O_2\), m=\(16g\)

Number of moles of \(O_2\), $$n=\frac{m}{M}$$ where \(M\)=molecular weight of \(O_2\)=\(32g\)
$$n=\frac{16}{32}=\frac{1}{2}$$

Temperature \(T=27^\circ=300K\)

If \(V_1\) be the original volume and \(V_2\) be the final volume

Work done by the gas in the isothermal process $$ W_0=nRTlog(V_2/V_1)$$$$=0.5*8.31*ln(3/4)$$$$=150*8.31*ln(3/4)$$$$=-358.56J$$

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