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 $$ W_0=nRTlog(V_2/V_1)$$$$=0.58.31ln(3/4)$$$$=1508.31ln(3/4)$$$$=-358.56J$$