Given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths, $A, B, C$ . Let $Q, W$ and $U$ represent the heat supplied to the gas, work done by the gas, and the internal energy of the gas, respectiely, then which of the following conditions is true?

$P-V$ diagram for two gases during adiabatic process are shown in the figure by curves $A$ and $B$ are for

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done is $W$. Then

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n = $ constant, then $n$ is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively)

A carnot engine, having an efficiency of $\eta  = 1/10$ as heat engine, is used as a refrigetator. If the work done on the system is $10\,J$ , the amount of energy absorbed from the reservoir at lower temperature is ………. $\mathrm{J}$