Question

For a particular heat engine, 3,000 J of energy goes in at 700 K and 2000 J comes out at 200 K. The rest of the energy is used to do useful work. What is the actual efficiency of this engine?
A. 0.71
B. 0.33
C. 0.67
D. 0.29
E. 1.5

Answer 1

The efficiency of the heat engine is always defined by the ratio of the work done to the heat absorbed. The work done by the heat engine is the difference between the heat absorbed and the heat rejected.

Complete step by step answer:
Given:
The energy that is observed by a heat engine is ${Q_A} = 3000\;{\rm{J}}$.
The energy that is rejected by the heat engine is ${Q_R} = 2000\;{\rm{J}}$.
The temperature of the energy absorbed by the heat engine is ${T_A} = 700\;{\rm{K}}$
The temperature of the energy rejected by the heat engine is ${T_R} = 200\;{\rm{K}}$
The equation to the efficiency of the heat engine is,
$\eta = \dfrac{{{Q_A} - {Q_R}}}{{{Q_R}}}$
Substitute the values in the above equation.

$$\eta = \dfrac{{{Q_A} - {Q_R}}}{{{Q_R}}}\\\ \Rightarrow\eta = \dfrac{{3000 - 2000}}{{3000}}\\\ \Rightarrow\eta = \dfrac{{1000}}{{3000}}\\\ \therefore\eta = 0.33$$

Therefore, the efficiency is 0.33 that means the option (b) is correct.

Note: Here, the efficiency of the heat engine should be taken as the work done to the heat absorbed, be sure the heat absorbed is defined as the energy that goes into the engine and the heat rejection is the energy that remains after the work is done by the engine.