Question

A Carnot engine works between 600K and 300K. In each cycle of operations, the engine draws 1000 Joule of energy from the source at 600K. The efficiency of the engine is
A. 20%
B. 50%
C. 70%
D. 90%

Answer 1

Hint: Carnot efficiency describes the maximum thermal efficiency that a heat engine can possess as given by the Second Law of Thermodynamics. The Second Law states that waste heat (sink of the heat) has to be produced in a thermodynamic process where the work is done by a heat source.

Complete step by step answer:
Carnot engine is a theoretical thermodynamic cycle that provides an estimate of the maximum possible efficiency that a heat engine can produce during the conversion process of heat into work and conversely, working between two reservoirs, can possess.The Carnot theorem states that “A system working between any two provided temperatures ${T_1}$ (hot reservoir) and ${T_2}$ (cold reservoir), can never achieve an efficiency which is more than that of the Carnot engine working between the same reservoirs, respectively.
The efficiency of the Carnot engine is given by the formula as below:
\[\eta = 1 - \dfrac{{{T_2}}}{{{T_1}}}\]
Here, ${T_2}$ is the cold reservoir that is the sink, while ${T_1}$ is the hot reservoir which is the source. Also, here\[\eta \] is the efficiency of the Carnot engine. Thus, the efficiency of the Carnot engine given above is;
\[
\eta = 1 - \dfrac{{300}}{{600}} \\
\therefore \eta = 0.5
\]
Thus, the efficiency of the Carnot engine is 50%.

Hence, option B is the correct answer.

Note:According to the Second law of thermodynamics, the efficiency of the engine cannot be 100% and there has to be wasted energy in the form of heat that has to be produced. A Carnot engine is just a theoretical engine which shows maximum efficiency, and the practical engines try to be as close to the efficiency of a Carnot engine as possible.