A heat engine operates between a $400$K reservoir and a $200$K

reservoir. It has an efficiency of $0\mathrm{.}20.$

a$)$ Determine the useful work it does if it extracts $1000$J from the

hot reservoir.

b$)$ Determine the heat expelled to the $200$K reservoir if it extracts

$1000$J from the hot reservoir and does the work you calculated

in part a$).$

c$)$ Someone claims they can make a heat engine operating between

these two temperatures that can do $600$J of work after extracting

$1000$J of heat from the hot reservoir. Is this possible? Why or why not?