The pressure of an ideal gas varies with volume as $P = \alpha V,$ where $\alpha$ is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes $m$ times its initial volume. The work done by the gas in the process is

$A$ thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are:
$P_A = 3 \times 10^4 \, Pa, \, P_B = 8 \times 10^4 \, Pa$ and $V_A = 2 \times 10^{-3} \, m^3, \, V_D = 5 \times 10^{-3} \, m^3$
In process $AB$,$600 \, J$ of heat is added to the system and in process $BC$,$200 \, J$ of heat is added to the system. The change in internal energy of the system in process $AC$ would be ...... $J$.

According to the $PV$ diagram shown in the figure,a thermodynamic system is taken from state $A$ to state $B$ along the path $ACB$ and is brought back to state $A$ along the path $BDA$. The net work done during the complete cycle is given by the area of:

An ideal gas is taken around the cycle $ABCA$ as shown in the $P-V$ diagram. The work done during the cycle is

$A$ thermodynamic system is taken through the cyclic process $ABC$ as shown in the figure ($P-V$ graph: $A(2, 100)$, $B(5, 300)$, $C(5, 100)$). The total work done by the system during the cycle $ABC$ is . . . . . . $J$.

The net work done by an ideal gas going through the cycle as shown in the $P-V$ diagram below is