The efficiency of a Carnot heat engine operating between absolute temperatures T₁ and T₂ (when, T₁ > T₂) is given by $$\frac{{{{\text{T}}_1} - {{\text{T}}_2}}}{{{{\text{T}}_1}}}.$$   The co-efficient of performance (C.O.P.) of a Carnot heat pump operating between T₁ and T₂ is given by

A. $$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_1} - {{\text{T}}_2}}}$$

B. $$\frac{{{{\text{T}}_2}}}{{{{\text{T}}_1} - {{\text{T}}_2}}}$$

C. $$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}}$$

D. $$\frac{{{{\text{T}}_2}}}{{{{\text{T}}_1}}}$$

Answer: Option A

Solution(By Examveda Team)

The efficiency of an heat engine is given by \[\mathop \eta \limits^\iota = \frac{{{Q_1} - {Q_2}}}{{{Q_1}}}\]
For heat pump it is given by \[\mathop \eta \limits^\iota = \frac{{{Q_1}}}{{{Q_1} - {Q_2}}}\]
Where \[{{Q_1}}\] and \[{{Q_2}}\] are given by heat taken and heat given to the thermal reservoirs respectively.
\[ \Rightarrow {\left( {\mathop \eta \limits^\iota } \right)_{heat\,\,engine}} = \frac{1}{{{{\left( {\mathop \eta \limits^\iota } \right)}_{heat\,\,pump}}}}\]