Question

Thermal efficiency = …………………… or$\dfrac{\text{Heat Utilised}}{\text{Heat Produced}}$
A.$\dfrac{{{Q_4}}}{{{Q_T}}}$
B.${Q_4} \times {Q_T}$
C.${Q_4} + {Q_T}$
D.${Q_4} - {Q_T}$

Answer 1

Hint: The given question is totally based on the concept of thermal efficiency. First of all we need to define thermal efficiency. If we know the concept of thermal efficiency, we can directly relate it with the given options in the above question. After that we can finally conclude with the correct solution for the given question.

Complete step by step answer:
Step one
First of all we need to define thermal efficiency.
So, we can define thermal efficiency of a heat engine as the ratio of the work done by the engine to the amount of heat supplied. Mathematically, we can write it as,
${\eta _T} = \dfrac{{{W_{out}}}}{{{H_{In}}}}$
Where,$W$denotes the work done by the heat engine and$H$denotes the amount of heat supplied to the heat engine.
Step two
In case of a heat pump, the thermal efficiency is defined as the ratio of net heat output required for heating to the amount of heat or energy supplied.
If we observe the options that are given in the question, then we can see that only option (A) is written in the form of a ratio. So, we can conclude that the required value of thermal efficiency is given by$\dfrac{{{Q_4}}}{{{Q_T}}}$.
Hence, option (A), i.e. $\dfrac{{{Q_4}}}{{{Q_T}}}$is the correct choice for the given question.

Note:
We can also define thermal efficiency as the percentage of heat energy transformed into work by a heat engine. Thermal efficiency is a dimensionless quantity. The thermal efficiency is calculated in heat engines such as steam engines or turbines, boilers, furnaces, refrigerators etc.