One mole of an ideal gas at initial temperature $T$ undergoes a quasi-static process during which the volume $V$ is doubled. During the process,the internal energy $U$ obeys the equation $U = a V^3$,where $a$ is a constant. The work done during this process is

$A$ cyclic process $ABCDA$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?

An engine (consisting of one mole of an ideal gas in a cylinder with a piston) follows the cycle shown in the figure. Find the heat exchanged by the engine with the surroundings in each part of the cycle. Given $C_V = \frac{3}{2}R$.
$(a)$ $A$ to $B$: Constant volume
$(b)$ $B$ to $C$: Constant pressure
$(c)$ $C$ to $D$: Adiabatic expansion
$(d)$ $D$ to $A$: Constant pressure

An ideal gas with pressure $P$,volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. The same gas is expanded adiabatically to a volume $2V$,the final pressure is $P_a$. In terms of the ratio of the two specific heats for the gas $\gamma$,the ratio $\frac{P_i}{P_a}$ is

Carbon monoxide is taken around the closed cycle $abc$. The process $bc$ is isothermal as shown in the figure. When the temperature of the gas is increased from $300 \ K$ to $1000 \ K$,it absorbs $7000 \ J$ of heat in going from $a$ to $b$. The heat released by the gas during the process $ca$ is ...... $J$.

In thermodynamic processes,which of the following statements is not true?