The system below uses two heat engines, where the waste heat from HE1 is used as the heat source for HE2.a) Find the overall efficiency of the system shown below as a function of the two individual efficiencies. In other words, find \( \eta_{\text{overall}} = f(\eta_1, \eta_2) \).b) Based on part a, can the efficiency of the two heat engines ever be greater than 100%? If multiple (infinite?) heat engines are chained together in the same way, so that each heat engine is powered by the waste heat of the one before it, can the overall efficiency ever be greater than 100%? The diagram illustrates a two-stage heat engine system, consisting of two heat engines, labelled HE1 and HE2.- **HE1** operates between a high temperature reservoir (denoted as \( T_H \)) and is supplied with heat energy \( \dot{Q}_H \). It generates work output \( \dot{W}_1 \).- **HE2** operates between \( HE1 \) and a low temperature reservoir (denoted as \( T_L \)). \( HE2 \) receives the transferred heat energy \( \dot{Q}_M \) at an intermediate temperature \( T_M \) and transfers heat \( \dot{Q}_L \) to \( T_L \) while producing work \( \dot{W}_2 \).Arrows represent the direction of heat and work flows. The cyclic arrows in HE1 and HE2 depict the cyclical nature of the engines' operation.

To Find : a) The overall efficiency of the system.Given : The Higher temperature is The Intermediated temperature is The Lower temperature is The Heat reject from the higher temperature is The Heat transferred to the second heat engine is The Heat reject to the lower temperature is The Work by first heat engine is The Work by the second heat engine isCalculation : The efficiency of heat engine 1 is, The efficiency of the heat engine 2 is, Multiply the equation number 1 and 2 is, The overall efficiency can be obtained as, Substitute the value in equation number 4 is, b) The overall efficiency can not be more then because, There will be some heat rejection Therefore Thus the overall efficiency never more thanThe overall efficiency of the system is

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a) Find the overall efficiency of the system shown below as a function of the two individual efficiencies. In other words, find n =f(n1,n2). overall ) Based on part a, can the efficiency of the two heat engines ever be greater than 100%? If multiple (infinite?) heat engines are chained together in the same way, so tha

a) Find the overall efficiency of the system shown below as a function of the two individual efficiencies. In other words, find n =f(n1,n2). overall ) Based on part a, can the efficiency of the two heat engines ever be greater than 100%? If multiple (infinite?) heat engines are chained together in the same way, so tha

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Question

The system below uses two heat engines, where the waste heat from HE1 is used as the heat source for HE2.

a) Find the overall efficiency of the system shown below as a function of the two individual efficiencies. In other words, find \( \eta_{\text{overall}} = f(\eta_1, \eta_2) \).

b) Based on part a, can the efficiency of the two heat engines ever be greater than 100%? If multiple (infinite?) heat engines are chained together in the same way, so that each heat engine is powered by the waste heat of the one before it, can the overall efficiency ever be greater than 100%?

The diagram illustrates a two-stage heat engine system, consisting of two heat engines, labelled HE1 and HE2.

- **HE1** operates between a high temperature reservoir (denoted as \( T_H \)) and is supplied with heat energy \( \dot{Q}_H \). It generates work output \( \dot{W}_1 \).

- **HE2** operates between \( HE1 \) and a low temperature reservoir (denoted as \( T_L \)). \( HE2 \) receives the transferred heat energy \( \dot{Q}_M \) at an intermediate temperature \( T_M \) and transfers heat \( \dot{Q}_L \) to \( T_L \) while producing work \( \dot{W}_2 \).

Arrows represent the direction of heat and work flows. The cyclic arrows in HE1 and HE2 depict the cyclical nature of the engines' operation.

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