Question

A scientist says that the efficiency of his heat engine which operates at source temperature 127°C and sink temperature 27°C is $26 \%$, then
A. It is impossible
B. It is possible but least probable
C. It is quite probable
D. Data are incomplete

Answer 1

Hint: This problem can be solved by using the concept of efficiency of a heat engine. Apply the formula for efficiency of a heat engine in terms of source temperature and sink temperature. Substitute the values of temperature in Kelvin in this formula and find the efficiency of the engine. Now, compare the calculated efficiency with the given efficiency and find the correct answer to this question.

Formula used:
$\eta=1-\dfrac {{T}_{2}}{{T}_{1}}$

Complete answer:
Given: Source temperature, ${T}_{1}= 127°C=400K$
            Sink temperature, ${T}_{2}= 27°C=300K$
Efficiency of a heat engine is given by,
$\eta=1-\dfrac {{T}_{2}}{{T}_{1}}$
Substituting values in the above equation we get,
$\eta=1- \dfrac {300}{400}$
$\Rightarrow \eta= 1-0.75$
$\Rightarrow \eta= 0.25$
$\Rightarrow \eta= 25 \%$
Thus, the efficiency of his heat engine is calculated to be $25\%$ so, attaining an efficiency of $26\%$ is not possible.

So, the correct answer is option A i.e. it is impossible.

Note:
Students should make sure that they convert the unit of temperature from Celsius to Kelvin by adding 273 to the temperature. Not converting the units may lead altogether to an incorrect solution. Efficiency of a heat engine can be increased by decreasing the temperature of the sink. Students must know that it is not possible to have an engine with $100\%$ efficiency. Efficiency of a heat engine can also be defined as the ratio of work done by the engine to the amount of heat drawn from the source.