(Solved): a handwritten solution would be preferred if possible... i will surely upvote... but plz answer in ...

a handwritten solution would be preferred if possible...
i will surely upvote...
but plz answer in an hour

 

The thermal efficiency of any heat engine cycle is given by: \[ \eta_{t h}=\frac{w_{n e t}}{q_{\text {in }}} \] Using this definition, prove that the thermal efficiency of a Diesel cycle is: \[ \eta_{t h, \text { Diesel }}=1-\frac{1}{r^{k-1}}\left\{\frac{r_{c}^{k}-1}{k\left(r_{c}-1\right)}\right\} \] where \( r=\frac{V_{1}}{V_{2}}, r_{c}=\frac{V_{3}}{V_{2}} \) and \( k=\frac{c_{p}}{c_{v}} \) Show all intermediate steps in the proof.