Two moles of a triatomic gas $\left(\gamma = \frac{4}{3}\right)$ at temperature $327^{\circ} C$ expands adiabatically such that its volume becomes $8$ times its initial volume. Later, the temperature of the gas is doubled in an isochoric process. The total work done in the two processes is ($R$ - universal gas constant). (in $R$)

Air in a cylinder is suddenly compressed by a piston,which is then maintained at the same position. With the passage of time,

Consider that an ideal gas ($n$ moles) is expanding in a process given by $P = f(V)$,which passes through a point $(V_0, P_0)$. Show that the gas is absorbing heat at $(P_0, V_0)$ if the slope of the curve $P = f(V)$ is larger than the slope of the adiabatic curve passing through $(P_0, V_0)$.

An ideal monoatomic gas is carried along the cycle $ABCDA$ as shown in the figure. The total heat absorbed during this process is (in $p_0 V_0$)

What are the limitations of the first law of thermodynamics?

Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal diatomic gas at temperature $T$ $K$. The piston of cylinder $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in cylinder $B$ is (where $\gamma = \frac{C_{P}}{C_{V}}$):