The internal energy  of a gas in an adiabatic process is given by $U=a+bPV$, find $\gamma :$

What would be the efficiency of the heat engine diagramed as shown below?

The figure shows two paths for the change of state of a gas from $A$ to $B$. The ratio of molar heat capacities in path $1$ and path $2$ is:-

A partition divides a container having insulated walls into two compartments $\mathrm{I}$ and $\mathrm{II}$. The same gas fills the two compartments whose initial parameters are given. The partition is a conducting wall which can move freely without friction. Which of the following statements is/are correct, with reference to the final equilibrium position?