Question

# A Carnot engine works between ice point and steam point. Its efficiency will be\begin{align} & \text{A}\text{. 85}\text{.42 }\!\%\!\!\text{ } \\ & \text{B}\text{. 71}\text{.23 }\!\%\!\!\text{ } \\ & \text{C}\text{. 53}\text{.36 }\!\%\!\!\text{ } \\ & \text{D}\text{. 26}\text{.81 }\!\%\!\!\text{ } \\ \end{align}

Hint: Define Carnot engine. A Carnot engine gives the maximum efficiency of an engine working between two temperatures. Obtain the mathematical expression for the efficiency of a Carnot engine. Put the given values on the obtained expression to find the answer.

A Carnot engine is a theoretical thermodynamic cycle which gives us the maximum possible efficiency of a heat engine working between two temperatures.
Efficiency of a Carnot engine can be defined as the ratio of the work done by the heat engine to the heat provided to the heat engine. The efficiency of a Carnot engine does not depend on the nature of the material used. It only depends on the temperature of the hot and cold reservoir of the Carnot engine.
The efficiency of Carnot engine can be mathematically expressed in terms of the temperature of the hot and cold reservoir of the system as,
$\eta =1-\dfrac{{{T}_{c}}}{{{T}_{h}}}$
Where, $\eta$ is the efficiency of the Carnot engine, ${{T}_{c}}$ is the temperature of the cold reservoir in kelvin and ${{T}_{h}}$ is the temperature of the hot reservoir in kelvin.
Now, the temperature of the ice point or the cold reservoir is,
${{T}_{c}}={{0}^{0}}C=273K$
Again, the temperature of the steam point or the boiling temperature is,
${{T}_{h}}={{100}^{0}}C=373K$
So, the efficiency of the Carnot engine working between the ice point and the steam point of the will be,
$\eta =1-\dfrac{273}{373}=1-0.7319=0.2681$
So, the percentage of efficiency of the Carnot engine will be,
$\eta =0.2681\times 100\%=26.81\%$

So, the correct answer is “Option D”.

Note:
The Carnot engine operates on a reversible Carnot cycle. Carnot cycle is a reversible process where four operations are involved. The processes involved in Carnot cycle are isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.