$A$ monatomic gas of volume $V$ and pressure $P$ expands isothermally to a volume $27 V$ and then is compressed adiabatically to a volume $V$. The final pressure of the gas is: (in $P$)

Which of the following statement$(s)$ is/are true? "Internal energy of an ideal gas ..........."

The efficiency of a thermodynamic cycle $1-2-3-1$ (see picture) is $20\%$ and for another thermodynamic cycle $1-3-4-1$ efficiency is equal to $10\%$. Determine the efficiency $\eta$ (in $\%$) of the thermodynamic cycle $1-2-3-4-1$. The gas is assumed to be ideal.

One mole of a gas expands such that its volume $V$ changes with absolute temperature $T$ in accordance with the relation $V = K T^2$,where $K$ is a constant. If the temperature of the gas changes by $60 \text{ K}$,then the work done by the gas is ($R$ is the universal gas constant).

In the $p-V$ diagram below,the dashed curved line is an adiabat. For a process that is described by a straight line joining two points $X$ and $Y$ on the adiabat (solid line in the diagram),heat is (Hint: consider the variation in temperature from $X$ to $Y$ along the straight line)

An ideal gas expands isothermally from volume $V_1$ to volume $V_2$. It is then compressed to the original volume $V_1$ adiabatically. If $p_1$ and $p_2$ represent the initial pressure and final pressure respectively, and $W$ represents the net work done by the gas during the entire process, then: