A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in Fig. 12.11. Find heat exchanged by the engine, with the surroundings for each section of the cycle. (Cv = (3/2) R)
AB: constant volume
BC: constant pressure
CD: adiabatic
DA: constant pressure
According to 1st law of thermodynamics which states that the change in internal energy of a system is equal to the heat added to the system minus work done by the system.
As process AB is isochoric Work done by the system is given by 
and for isochoric process it is 
........(1)
And we know 
Where, n = No. Of moles i.e. one in this case
Cv= Specific heat capacity at constant volume i.e. 
in this case
= Change in temperature
= 
........(2)
Using Ideal gas eq. i.e. PV=nRT
We can replace R
by PBVB and R
by PAVA
VA = VB (Given in the question)
Substituting the values in eq. 2 we get
= 
Using eq. 1
Q= 
Now Process BC is isobaric i.e. Constant Pressure
Work done by the system is given by 
as P is constant
W = 
= 
(
)
We know 
by 1st law of thermodynamics
Q = 
+ 
since, 
Here n = 1 mole
Cv= 
R
= 
+
(
)
Using Ideal gas eq. i.e. PV=nRT
We can replace R
by PCVC and R
by PBVB
PB = PC (Given in the question)
=
+
(
)
Q = 
Process CD is adiabatic
=0
Again Process AD is isobaric i.e Constant Pressure
Work done by the system is given by 
as P is constant
W = 
= 
(
)
We know 
by 1st law of thermodynamics
Q = 
+ 
since, 
Here n = 1 mole
Cv= 
R
= 
+
(
)
Using Ideal gas eq. i.e. PV=nRT
We can replace R
by PAVA and R
by PDVD
PA= PD (Given in the question)
=
+
(
)
Q = 
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