Paper Homework $5($to be turned in before class on Friday, September $27)$

The picture below shows the cycle of an engine using $n$ moles of a diatomic ideal gas $(5$ degrees of freedom$).$ The process between b and c is adiabatic. The state parameters at b are $p_o,V_o,$ and $T_o.$ The volume at c is $2V_o.$

a$)$ For the engine to work, in which direction $($clockwise or counterclockwise$)$ should the gas move around the cycle?

b$)$ Find the values of pressure and temperature at a and c$.$

c$)$ Find the heat $Q$ transferred into the gas for each process.

d$)$ Find the efficiency of the engine.

Write your results in terms of $R,n,p_o,V_o,$ and $T_o.$