Numerical based on the Efficiency of a heat engine – solved

Let’s solve a selected Numerical problem based on the Efficiency of a heat engine.

Formula Used

Efficiency is defined as the ratio of the net work done by the engine to the amount of heat that must be supplied to accomplish this work.
Efficiency Formula: e = W/Q_H
where e is the efficiency, W is the net work done by the engine, and Q_H is the quantity of heat taken in by the engine.

Numerical problem on heat engine efficiency

Question 1] A heat engine takes in 1200 J of heat from the high-temperature heat source in each cycle and does 400 J of work in each cycle.
a. What is the efficiency of this engine?
b. How much heat is released into the environment in each cycle?

Solution:

a) Q_H = 1200 J
W = 400 J
e = ?

e = W/Q_H = 400/1200 = 1/3 = 0.33 = 33 %

b) Q_c = Q_H – W
=>Q_c = 1200 – 400 J = 800 J

Facts:

Heat is taken in at high temperatures, T_H. Some heat is converted to work, and the remainder is released at a lower temperature, T_C.