[ $R$ 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 $\left|\frac{Q_{U \rightarrow 2}}{Q_{3 \rightarrow 4}}\right|=\frac{1}{2}$