The efficiency of a Carnot heat engine operating between absolute temperatures T1 and T2 (when, T1 > T2) is given by T_1 - T_2T_1. The co-efficient of performance (C.O.P.) of a Carnot heat pump operating between T1 and T2 is given by

The efficiency of an heat engine is given by [mathop limits^ = Q_1 - Q_2Q_1] For heat pump it is given by [mathop limits^ = Q_1Q_1 - Q_2] Where [Q_1] and [Q_2] are given by heat taken and heat given to the thermal reservoirs respectively. [ ( mathop limits^ )_heatengine = 1( mathop limits^ )_heatpump]

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Chemical Engineering Thermodynamics

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 & Solution

Correct Answer: Option A

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.
\[ \Rightarrow {\left( {\mathop \eta \limits^\iota } \right)_{heat\,\,engine}} = \frac{1}{{{{\left( {\mathop \eta \limits^\iota } \right)}_{heat\,\,pump}}}}\]

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The efficiency of a Carnot heat engine operating between absolute temperatures...

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

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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