$A$ thermodynamic system goes from states $(i) \, P_1, V$ to $2P_1, V$ and $(ii) \, P, V$ to $P, 2V$. The work done in the two cases is:

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.

$2$ moles of an ideal monoatomic gas is carried from a state $(p_{0}, V_{0})$ to state $(2 p_{0}, 2 V_{0})$ along a straight line path in a $p-V$ diagram. The amount of heat absorbed by the gas in the process is given by

One mole of a monatomic ideal gas is taken through a cycle $ABCDA$ as shown in the $P-V$ diagram. Column $II$ gives the characteristics involved in the cycle. Match them with each of the processes given in Column $I$.

Column $I$	Column $II$
$(A)$ Process $A \rightarrow B$	$(p)$ Internal energy decreases.
$(B)$ Process $B \rightarrow C$	$(q)$ Internal energy increases.
$(C)$ Process $C \rightarrow D$	$(r)$ Heat is lost.
$(D)$ Process $D \rightarrow A$	$(s)$ Heat is gained.
	$(t)$ Work is done on the gas.

$A$ thermodynamic system undergoes a cyclic process through four stages. The energy values involved during this process are $Q_1 = 600 \ J, Q_2 = -400 \ J, Q_3 = -300 \ J$,and $Q_4 = 200 \ J$. The work values are $W_1 = 300 \ J, W_2 = -200 \ J, W_3 = -150 \ J$,and $W_4$. Find the value of $W_4$ in $J$.

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