Question

Consider the cyclic process depticted in figure. If Q is negative for the process BC, and If $\Delta U$ is negative for the process CA, what are the signs of Q, W and $\Delta U$ that are associated with each process ?

Answer 1

First law of thermodynamics : $Q=dU+W$

As $dV$ in process $BC$ is zero $⟹$ $W_{BC}=0$

$Q_{BC}<0$ $⟹$ $d{U}_{BC}<0$

Process CA : $d{U}_{CA}<0$

As $dv<0$ for the process CA, $⟹$ $W_{CA}<0$

Thus $Q_{CA}=d{U}_{CA}+W_{CA}<0$

Process AB :

As $d{U}_{cycle}=d{U}_{AB}+d{U}_{BC}+d{U}_{CA}=0$

But $d{U}_{CA}<0$, $d{U}_{BC}<0$ $⟹d{U}_{AB}>0$

Also $W_{AB}=W_{expansion}>0$ $(\because dv>0)$ for $AB$

Thus $Q_{AB}=d{U}_{AB}+W_{AB}>0$