Question

A heat engine carries one mole of an ideal mono-atomic
gas around the cycle as shown in figure, the amount of
heat added in the process AB and heat removed in the
process CA are:



please give reasons: and proper formulae​

Answer 1

for process A -- B :

The process AB is isochoric process, because volume remains constant.

so, when we add heat to system, it goes to increase their internal energy.

i.e., ∆U = ∆Q

so, head added at constant volume , ∆Q = $nC_v\Delta T$

here n = 1, $C_v$ = 3R/2 [ because, gas is monoatomic ]

and ∆T = (600 - 300)K = 300K , R = 25/3 J/K.mol

so, heat added in the process AB , ∆Q = 1 × 3R/2 × 300 = 900R/2 = 450 × 25/3

= 3750 Joule

for process CA :

this is isobaric process because pressure remains constant.

heat at constant pressure , ∆Q = ∆U + w

= $nC_p\Delta T'$

where $C_p$ = 5R/2

then, heat removed in process CA, ∆Q = 1 × 5R/2 × (300K-450K)

= - 1 × 5/2 × 25/3 × 150 Joule

= - 125/6 × 150 joule

= - 3125 Joule [ here negative sign indicates heat is removed ]