# 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= 400/1200 = 1/3 = 0.33 = 33 %_{H}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}.