TITLE.PM5

248 ENGINEERING THERMODYNAMICS

dharm
/M-therm/th5-2.pm5

T

(300 K)

2 T

(600 K)

1

Carnot

refrig.

Carnot

engine

T 3

Q 1 ′′ Q 1 ′

Wcarnot= Q – Q 1 1 ′

Q 2 Q 1

Fig. 5.18

Efficiency of Carnot engine,

ηcarnot engine = QQ

Q

11

1

−′ = TT

T

13

1

−

=

Work of Carnot engine

Heat supplied to the Carnot engine =

W

Q

carnot

1

or WQTT
carnot T
= −
F
HG

I

(^1) KJ
13
1
...(i)
Also C.O.P.(carnot refrigerator) =
Q
QQ
2
12 ′′−
= T
TT
2
32 −
==Heat absorbed
W
Q
carnot Wcarnot
2
or Wcarnot = Q
TT
(^2) T
32
2
F −
HG
I
KJ
...(ii)
(i)Temperature, T 3 :
From eqns. (i) and (ii), we get
Q TT
(^1) T
13
1
F −
HG
I
KJ
= Q
TT
(^2) T
32
2
F −
HG
I
KJ
∴
Q
Q
T
T
TT
TT
2
1
2
1
13
32
= −
−
F
HG
I
KJ
or
Q
Q
2
1
= 1 =
300
600
600
300
3
3
−
−
F
HG
I
KJ
T
T
or 600 – T 3 = 2(T 3 – 300)
600 – T 3 = 2T 3 – 600 or T 3 = 400 K
Hence, temperature, T 3 = 400 K. (Ans.)