$[14\mathrm{.}4]$ Consider a heat engine containing helium as its $$working fluid$$ that

undergoes the following processes: from an initial temperature of $140$ C at

$200$ kPa and volume of $4\mathrm{.}0$ liters:

$(1)$ heat is added at constant volume until the pressure is $800$ kPa.

$(2)$ the gas expands adiabatically until the pressure reaches $200$ kPa.

$(3)$ the gas is then compressed at constant pressure back to its original vol$-$

ume.

$($a$)$ During which stages did the gas do positive work? When did the gas

have work done on it$?$

$($b$)$ During which stages was heat added to the gas? When was heat released

from the gas?

$($c$)$ What is the net work done by the gas during one cycle?

Recall that during an adiabatic process, the relationship between P and

V is P V $=$ constant with $=5/3$ for monatomic gases like helium.