Question

A sample of one mole of an ideal gas having $\gamma =7/5$ is heated at a constant pressure. If the heat absorbed by the gas is $21J$. Determine the work done by the gas in Joule?

Answer 1

$\Delta Q=n{C}_p(T_2-T_1)=21J$

$\Delta V=n{C}_v(T_2-T_1)$

$=\frac{C_v}{C_p}n{C}_p(T_2-T_1)$

$\Delta V=\frac{1}{V}\times \Delta Q$

Work done $=\Delta Q-\Delta V$

$=\Delta Q-\frac{\Delta Q}{V}$

$=\Delta Q\left(\frac{V-1}{V}\right)$

$=21\left(\frac{1.4-1}{1}\right)$

$=8.4Joule$