TITLE.PM5

608 ENGINEERING THERMODYNAMICS

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(ii)The volume at the end of isothermal expansion, V 2 :

Heat transferred during isothermal expansion

p

V

T 2

Isentropics

Isotherms

T 1

1

2

3

4

T

s

12

4 3

T-s diagram

p-V diagram

Fig. 13.3. Carnot cycle.

= p 1 V 1 ln(r) = mRT 1 ln

V

V

2

1

F

HG

I

KJ

= 40 × 10^3 ...... (Given)

or 0.5 × 287 × 585.4 ln V^2
012.

F

HG

I

KJ

= 40 × 10^3

or ln V^2

120.

F

HG

I

KJ

=

40 10

0 5 287 585 4

×^3
..××
= 0.476
or V 2 = 0.12 × (e)0.476 = 0.193 m^3. (Ans.)
(iii)The heat transfer for each of the four processes :
Process Classification Heat transfer
1—2 Isothermal expansion 40 kJ
2—3 Adiabatic reversible expansion zero
3—4 Isothermal compression – 40 kJ
4—1 Adiabatic reversible compression zero. (Ans.)
+Example 13.3. In a Carnot cycle, the maximum pressure and temperature are limited
to 18 bar and 410°C. The ratio of isentropic compression is 6 and isothermal expansion is 1.5.
Assuming the volume of the air at the beginning of isothermal expansion as 0.18 m^3 , determine :
(i)The temperature and pressures at main points in the cycle.
(ii)Change in entropy during isothermal expansion.
(iii)Mean thermal efficiency of the cycle.
(iv)Mean effective pressure of the cycle.
(v)The theoretical power if there are 210 working cycles per minute.