[ $R$ is the gas constant]
$(1)$ Work done in this thermodynamic cycle $(1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1)$ is $| W |=\frac{1}{2} RT _0$
$(2)$ The ratio of heat transfer during processes $1 \rightarrow 2$ and $2 \rightarrow 3$ is $\left|\frac{ Q _{1 \rightarrow 2}}{ Q _{2 \rightarrow 3}}\right|=\frac{5}{3}$
$(3)$ The above thermodynamic cycle exhibits only isochoric and adiabatic processes.
$(4)$ The ratio of heat transfer during processes $1 \rightarrow 2$ and $3 \rightarrow 4$ is $\left|\frac{Q_{U \rightarrow 2}}{Q_{3 \rightarrow 4}}\right|=\frac{1}{2}$
| Process | Condition |
| $(I)$ Adiabatic | $(A)\; \Delta W =0$ |
| $(II)$ Isothermal | $(B)\; \Delta Q=0$ |
| $(III)$ Isochoric | $(C)\; \Delta U \neq 0, \Delta W \neq 0 \Delta Q \neq 0$ |
| $(IV)$ Isobaric | $(D)\; \Delta U =0$ |



