Carbon monoxide is carried around a closed cyclic process abc, in which bc is an isothermal process, as shown in figure. The gas absorbs 7000 J of heat as its temperature is increased from 300 K to 1000 K in going from a to b. The quantity of heat ejected by the gas during the process ca is

${\mathrm{Q}}_{\mathrm{ab}}=+7000={\mathrm{\mu C}}_{\mathrm{v}}(1000-300)$ …….(i)

For the process ca:

$\begin{array}{l}{\mathrm{T}}_{\mathrm{a}}=300\mathrm{K},{\mathrm{T}}_{\mathrm{c}}={\mathrm{T}}_{\mathrm{b}}=1000\mathrm{K}\\ {\mathrm{Q}}_{\mathrm{ca}}={\mathrm{\mu C}}_{\mathrm{p}}(300-1000)=-{\mathrm{\mu C}}_{\mathrm{p}}\times 700\\ =-\mathrm{\mu }\left({\mathrm{C}}_{\mathrm{v}}+\mathrm{R}\right)700 ..........\left(\mathrm{ii}\right)\end{array}$

For carbon monoxide:

$\begin{array}{l}{\mathrm{T}}_{\mathrm{a}}=300\mathrm{K},{\mathrm{T}}_{\mathrm{c}}={\mathrm{T}}_{\mathrm{h}}=1000\mathrm{K}\\ (\mathrm{\Delta Q}{)}_{\mathrm{ca}}={\mathrm{\mu C}}_{\mathrm{p}}(300-1000)=-{\mathrm{\mu C}}_{\mathrm{p}}\times 700\\ =-\mathrm{\mu }\left({\mathrm{C}}_{\mathrm{v}}+\mathrm{R}\right)700\end{array}$

For carbon monoxide: $\mathrm{\gamma }=\frac{7}{5}$

${\mathrm{C}}_{\mathrm{v}}=\frac{\mathrm{R}}{\mathrm{\gamma }-1}=\frac{\mathrm{R}}{\frac{7}{5}-1}=\frac{5\mathrm{R}}{2}$ …………..(iii)

Hence, from Eq. (i)

$\begin{array}{l}7000=\mathrm{\mu }\frac{5\mathrm{R}}{2}\times 700\text{ or }\mathrm{\mu R}=\frac{20}{5}=4\\ {\mathrm{Q}}_{\mathrm{ca}}=-(7000+4\times 700)=-9800\mathrm{J}\end{array}$

Negative sign shows that heat is ejected.