Question

The efficiency of heat engine is maximum when:
A. Temperature of sink > temperature of source
B. Temperature of source > temperature of sink
C. The difference between temperature of source and sink is very high.
D. None of these

Answer 1

Hint:The heat engine transfers thermal energy from a hotter body to a colder body. As the temperature of the hotter body will remain high and the colder body will remain low, a high amount of thermal energy will be transferred. A high amount of work will be done.

Complete answer:
The system which converts the thermal energy to mechanical energy is known as a heat engine.Heat engine has a heat source which gives the thermal energy to the working substance to a high temperature. The working substance is done work and transfers the heat to the colder body. The hotter body is known as the source and the colder body is known as the sink.So, the thermal energy that is the heat given by the source is utilized in doing work, and some of the heat transfer to the sink, and some amount of heat wasted as it lost to the surrounding.The efficiency of the heat engine is defined as the amount of heat out of the total heat that is converted to the work.
The formula of efficiency is as follows:
\[\eta = \,\dfrac{{{{\text{T}}_{{\text{source}}}} - {{\text{T}}_{{\text{sink}}}}}}{{{{\text{T}}_{{\text{source}}}}}}\]
Where,
\[\eta \] is the efficiency.
\[{{\text{T}}_{{\text{source}}}}\] is the temperature of the source.
\[{{\text{T}}_{{\text{sink}}}}\] is the temperature of the sink.
According to the efficiency formula, efficiency is directly proportional to the temperature difference.Heat is transferred to the sink so the temperature of the sink is also increased. As the temperature difference will be high, the efficiency of the heat engine will be high.So, the efficiency of the heat engine is maximum when the difference between the temperature of the source and sink is very high.

Therefore, option (C) the difference between the temperature of source and sink is very high, is correct.

Note:Remember that efficiency is defined as the ratio of output to the input. The input is heat $q$ and output is the work $w$ so, the formula of efficiency is, \[\eta = \,\dfrac{w}{q}\]. Work depends upon the temperature difference. As the temperature difference will be high , the high amount of heat will be transferred, so a high amount of work will be done.