The correct options are
A Uc>Ub>Ua
B Uc−Ub=3RT0
C Uc−Ua=9RT02
D Ub−Ua=3RT02
Internal energy is a state function.(Doesnot depend on path)
We know, ΔU=nCvΔT
From a to b, pressure is contant
⇒V∝T
Volume changes from Vo to 2Vo
⇒ temperature changes from To to 2To .
For a monoatomic gas, Cv=32R
Ub−Ua=nCvΔT
=1×32R(2To−To)=32RTo....(i)
Option (d) is correct
From b to c, volume is constant.
⇒P∝T
Pressure changes from Po to 2Po
⇒ temperature changes from 2To to 4To.
Uc−Ub=nCvΔT
=1×32R(4To−2To)=3RTo....(ii)
Option (b) is correct
Also option (a) is correct
For c to a, we add equations (i) and (ii)
Uc−Ua=(Uc−Ub)+(Ub−Ua)
=3RTo+32RTo=9RT02
Option (c) is also correct.