The value of log$$_{10}$$ K for a reaction $A \rightleftharpoons B$ is

(Given : $${\Delta _r}H{^\circ _{298\,K}} = - 54.07$$ kJ mol$$^{-1}$$, $${\Delta _r}S{^\circ _{298\,K}} = 10$$ J K$$^{-1}$$ mol$$^{-1}$$ and R = 8.314 J K$$^{-1}$$ mol$$^{-1}$$; 2.303 $$\times$$ 8.314 $$\times$$ 298 = 5705)

A monatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?

The direct conversion of A to B is difficult; hence, it is carried out by the following shown path:Given,

$$ \begin{aligned} & \Delta \mathrm{S}_{(\mathrm{A} \rightarrow \mathrm{C})}=50 \text { e.u. } \\ & \Delta \mathrm{S}_{(\mathrm{C} \rightarrow \mathrm{D})}=30 \text { e.u. } \\ & \Delta \mathrm{S}_{(\mathrm{B} \rightarrow \mathrm{D})}=20 \text { e.u. } \end{aligned} $$

Where e.u. is entropy unit. Then $\Delta \mathrm{S}_{(\mathrm{A} \rightarrow \mathrm{B})}$ is :