$(2)$ The figure shows many different paths for a system. We are told that when the system is taken from state $i$ to state $f$ along path iaf, $Q=50$cal and $W=20$cal. Along path ibff,$Q=36$ cal $.($You may give all your answers in cal below; you do not need to convert to J$).$

a$)$ What is $W$ along path ibf $?$

b$)$ If $W=-13$cal for the return path $fi,$ what is $Q$ for this path?

c$)$ If $E_{{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}},}i=10$cal, what is $E_{{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}}f?$

d$)$ If $E_{\text{i}\text{n}\text{t},},b=22$cal, what is $Q$ for path $ib$ and path $bf?$