Question

3. An ideal Carnot engine has an input of 150 J of heat per cycle at its high-temperature reservoir, which is maintained at 135 °C. The engine has a thermal efficiency of 22.0%. a. How much work does this engine do per cycle? b. How much heat does this engine output to its low-temperature reservoir per cycle? c. What is the temperature of the low-temperature reservoir? d. How many cycles would this engine have to go through to lift a 500-kg rock through a height of 100 m? e. Briefly discuss why the Carnot engine cannot be built. Be specific in your answer.

Answer 1

3)

given
Q_in = 150 J
temperature of hot reservoir, Th = 135 C = 135 + 273 = 408 K
efficiency, n = 225 = 0.22

a) we know, n = Wordkone/Q_in

Workdone = n*Q_in

W = 0.22*150

= 33 J <<<<<<<--------------------Answer

b) Q_out = Q_in - W

= 150 - 33

= 117 J <<<<<<<--------------------Answer

c) let Tc is the temperature of the low-temperature reservoir

now use, n = 1 - Tc/Th

Tc/Th = 1 - n

Tc = (1 - n)*Th

= (1 - 0.22)*408

= 318.2 K

= 318.2 - 273

= 45.2 C

d) number of cycles, N = Energy required to lift/Work done by engine per cycle

= m*g*h/W

= 500*9.8*100/33

= 14848

e) Carnot engine is an ideal heat engine.

which is made up of perfect conductors and perfect insulator.

As we do not have ideal conductors and ideal insulators, we can not built carnot engine.

carnot is an ideal and hypothetical engine which can not be built practically.