Question

Two moles of a certain gas at a temperature $T_o=300K$ were cooled isochorically so that the pressure of the gas reduced $2$ times. Then as a result of isobaric process, the gas is allowed to expand till its temperature go back to the initial value. The total amount of heat absorbed by gas (in $J$) in this process is $X\times 500$.The value of X is:

Answer 1

Consider all the states of the system:

• $P_o,V_0,300K$
• $\frac{P_o}{2},V_o,150K$
• $\frac{P_o}{2},2V_o,300K$

i.e Work done = $W_{isochoric}+W_{isobaric}$
Work done = $0+P(V_2-V1)$
$w=\frac{P_o}{2}(2V_o-V_o)=\frac{P_0{V}_0}{2}$
also
Gas equation:
$PV=nRT$
$P_o{V}_o=2\times 8.314\times 300=5000J$
i.e. $w=\frac{P_o{V}_o}{2}=\frac{5000}{2}=2500J$