Question

19 - 3 -4

A heat engine operates between a reservoir at 29°C and one at 341°C.

What is the maximum efficiency possible for this engine?

heat engine operates in a Carnot cycle between 88.0°C and 345°C. It absorbs 21,200 J of energy per cycle from the hot reservoir. The duration of each cycle is 3.00 s.

(a) What is the mechanical power output of this engine?
kW

(b) How much energy does it expel in each cycle by heat?

Answer 1

Question 1

Temperature of the hot reservoir = T_h = 341 ^oC = 341 + 273 K = 614 K

Temperature of the cold reservoir = T_c = 29 ^oC = 29 + 273 K = 302 K

Maximum possible efficiency of the engine =

Maximum possible efficiency is the carnot efficiency.

= 0.508

= 50.8%

Maximum possible efficiency of the engine = 50.8%

Question 2

Temperature of the hot reservoir = T_h = 345 ^oC = 345 + 273 K = 618 K

Temperature of the cold reservoir = T_c = 88 ^oC = 88 + 273 K = 361 K

Efficiency of the carnot engine =

= 0.41586

Energy absorbed by the carnot engine per cycle from the hot reservoir = Q_h = 21200 J

Work done by the carnot engine per cycle = W

Energy the carnot engine expels in each cycle = Q_c

W = 8816 J

Q_h = W + Q_c

21200 = 8816 + Q_c

Q_c = 12384 J

Time period for each cycle = t = 3 sec

Power output of the engine = P

W = Pt

8816 = P(3)

P = 2939 W

P = 2.939 kW

a) Mechanical power output of the engine = 2.939 kW

b) Amount of energy the engine expels in each cycle = 12384 J