The initial pressure and volume of a given mass of an ideal gas (with $\frac{C_{p}}{C_{V}}=\gamma$), 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?

• A
  $0$
• B
  $(2^{\gamma-1}-1) \frac{p_{0} V_{0}}{\gamma-1}$
• C
  $\gamma p_{0} V_{0} \ln 2$
• D
  $\frac{p_{0} V_{0}}{2(\gamma-1)}$