
Step $1$ It is first compressed adiabatically from volume $V_{1}$ to $1 \;m ^{3}$.
Step $2$ Then expanded isothermally to volume $10 \;m ^{3}$.
Step $3$ Then expanded adiabatically to volume $V _{3}$.
Step $4$ Then compressed isothermally to volume $V_{1}$. If the efficiency of the above cycle is $3 / 4$, then $V_{1}$ is ............ $m^3$

$(A)$ If $V_2=2 V_1$ and $T_2=3 T_1$, then the energy stored in the spring is $\frac{1}{4} P_1 V_1$
$(B)$ If $V_2=2 V_1$ and $T_2=3 T_1$, then the change in internal energy is $3 P_1 V_1$
$(C)$ If $V_2=3 V_1$ and $T_2=4 T_1$, then the work done by the gas is $\frac{7}{3} P_1 V_1$
$(D)$ If $V_2=3 V_1$ and $T_2=4 T_1$, then the heat supplied to the gas is $\frac{17}{6} P_1 V_1$
