Problem $2$: $(10$ pts$)$ A path for a reversible Thermodynamic cycle is shown on the $T-S$ diagram below. With a properly scaled diagram, the cycle forms the shape of a perfect circle with a radius given below in terms of $S$ and $T($defined on the diagram$).$ The center of the circle is at $T=350K$ and $S=4k\frac{J}{K}.$

$r=2=\sqrt[\phantom{2}]{(\frac{S}{1\frac{kJ}{K}}{)}^2+(\frac{T}{25(K)}{)}^2}$

$($a$)$ If this cycle is run as a heat engine, how much work is produced per cycle?

$($b$)$ What is the efficiency of this heat engine?