A salesman claims that he has a very efficient, high temperature engine which ca

Question

A salesman claims that he has a very efficient, high temperature engine which can receive 1MJ heat input at 1000 C, produce 800 kJ of work and reject only 200 kJ heat to the surroundings at a temperature of 27 C. Answer the three parts below.
There are five parts, (a) through (e).
(2) (a) Is the First Law of Thermodynamics satisfied here? Justify your answer.

(3) (b) What is efficiency of the above engine?

(4) (c) Is the claim of the salesman, as it is given in the problem statement at the top of this page, valid? Justify your answer.

(3) (d) If there is a reversible refrigerator operating under identical temperature conditions as the engine (that is, TH = 1000 C and TL = 27 C), what will be its coefficient of performance?

(3) (e) If there is a reversible heat pump operating under identical temperature conditions as the engine (that is, TH = 1000 C and TL = 27 C), what will be its coefficient of performance?

Explanation / Answer

SINCE Q= U+W

Q= 800KJ+200KJ= 1000KJ= 1MJ

SINCE ITS GIVEN TOO

SO ITS SATISFIED

N= HEAT TAKEN- HEAT REJECTED/HEAT TAKEN

= WORKDONE/HEAT TAKEN

= 800/ 1000= .8

FOR MAXM EFFICIENCY

WE HAVE

N= 1- TCOLD/THOT=1-27/100O

= 1- .027= .973

HENCE HIS CLAIM FOR MAXM EFFICIENCY IS NOT VALID

D) COP OF REFRIGERATOR= THOT/ THOT-TCOLD

        = 1000/1000-27

        =1.027

E) COP OF HEAT PUMP= THOT/ THOT-TCOLD

        = 1000/1000-27

        =1.027

SINCE REFRIGERATOR AND HEAT PUMP ARE SAME

BOTH PERFORM SAME WORK

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