An ideal gas undergoes the cyclic process $abca$ as shown in the given $p-V$ diagram.

It rejects $50 \mathrm{J}$ of heat during $ab$ and absorbs $80 \mathrm{J}$ of heat during $ca$. During $bc$, there is no transfer of heat and $40 \mathrm{J}$ of work is done by the gas. What should be the area of the closed curve $abca ?$

The initial pressure and volume of a given mass of an ideal gas with $\left(\frac{C_p}{C_V}=\gamma \right)$, taken in a cylinder fitted with a piston, are $p_0$ and $V_0$ respectively. At this stage the gas has the same temperature as that of the surrounding medium which is $T_0.$ It is adiabatically compressed to a volume equal to $\frac{V_0}{2}.$
Subsequently the gas is allowed to come to thermal equilibrium with the surroundings. What is the heat released to the surrounding?