Acarnot heat engine receives 3,200 kj/s of heat from a high temperature source at 825 ℃ and rejects heat to a cold temperature sink at 15 ℃. solve following questions:

a. what is the thermal efficiency of this engine?
b. what is the power delivered by the engine in watts?
c. at what rate is heat rejected to the cold temperature sink?
d. what is the entropy change of the sink?

Explanation:

Given:

source temperature T1= 825° C = 1099 K

Sink temperature T2= 15°C = 288 K

Heat Supplied to the engine Qs= 3200 KW

a) Efficiency of a Carnot engine is

=0.7379

=73.79%

b)

let W be the powe delivered

W= 2361.408 KW

c) Heat rejected to the cold temperature Qr= Qs-W

= 3200-2361.408=838.60 KW

d) Entropy change in the sink

=838.60/288= 2.911 W/K

a.

b.

c.

d.

Explanation:

Given:

a.

Since the engine is a Carnot engine:

b.

Now the power delivered:

since here we are given with the rate of heat transfer

c.

rate of heat rejection to the sink:

d.

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s