$[3]$ A heat engine is reported to operate with $25\%$ efficiency when the cold reservoir is at $0^(0)$C$.$

$($a$)$ Assuming this engine follows the Carnot cycle, what is the temperature of the hot reservoir?

T$\_($H$)=$

$($b$)$ Suppose the heat input to this engine was $10$ J $.$ Calculate the work done by this engine.

W$=$

$($c$)$ Suppose the heat input to this engine was $10$J$.$ Calculate the heat rejected by this engine.

Q$\_($c$)=$

NOTE: I am taking an non$-$calculas physics course