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iit009 (24)

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An ideal monoatomic gas is used to operate an engine.P-V diagram of the cycle is clockwise rectangle with opposite vertices (V,P) and (3V,2P) and sides parallel to the axes .Calculate the efficiency of the cycle and compare its efficiency with the Carnot cycle over the same temperature range.
    
joyfrancis (1504)

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Easy..just keep on calculating the Q values for processes a-b, b-c,c-d and d-
 
a..neglect the negative values and add the positive ones...the net work done is
 
4pv...by area of rectangle, so efficiency would be 4pv divided by the sumation of
 
positive values of Q.
 
The answer comes out to be 2/5..i.e 40% efficiency
 
Please tell if someone is getting the same answer ?

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iit009 (24)

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but answer is 4/23 and 24/115
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iit009 (24)

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but ans is 4/23 and 24/115
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priyesh (1586)

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Let A be (V,P) , B be (V,2P) C be (3V,2P) and D be (3V,P)
 
so process given is ABCDA
 
work done = WBC + WDA = 4PV - 2PV = 2PV =2nRT
 
Qin = QAB + QBC = nCvT + nCp4T = 23/2 nRT   (use Cv = 3R/2)
 
hence efficiency = work done / Qin = 4/23

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bhupesh (606)

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Input is the heat supplied and out put is the work done its mono atomic gas hence you can find degree of freedom hence  the once the is know you can find out Cv   once Cv is know you find out the internal energy and by using first law of thermodynamics you find the heat supplied as well as work done.

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