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Mechanical Properties Of Fluids

Question
CBSEENPH11020305

Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in the figure. Efficiency of this cycle is nearly:(Assume the gas to be close to ideal gas)

  • 15.4%

  • 9.1%

  • 10.5%

  • 12.5%

Solution

A.

15.4%

The efficiency of a process is defined as the ratio of work done to energy supplied.
Here,straight eta space equals space fraction numerator increment straight W over denominator increment straight Q end fraction space equals space fraction numerator Area space under space straight p minus straight V space diagram over denominator increment straight Q subscript AB plus space increment straight Q subscript BC end fraction
Where Cp and Cv are two heat capacities (molar)
therefore space space fraction numerator straight p subscript straight o straight V subscript straight o over denominator nC subscript straight v increment straight T subscript 1 space plus nC subscript straight p space increment straight T subscript 2 end fraction
space equals fraction numerator straight p subscript straight o straight V subscript straight o over denominator begin display style 3 over 2 end style nR left parenthesis straight T subscript straight B minus straight T subscript straight A right parenthesis plus begin display style 5 over 2 end style nR left parenthesis straight T subscript straight C minus straight T subscript straight D right parenthesis end fraction
equals space fraction numerator straight p subscript straight o straight V subscript straight o over denominator begin display style 3 over 2 left parenthesis 2 straight p subscript straight o straight V subscript straight o minus straight p subscript straight o straight V subscript straight o right parenthesis plus 5 over 4 left parenthesis 4 straight p subscript straight o straight V subscript straight o minus 2 straight p subscript straight o straight V subscript straight o right parenthesis end style end fraction
equals space fraction numerator straight p subscript straight o straight V subscript straight o over denominator begin display style 3 over 2 straight p subscript straight o straight V subscript straight o plus 5 over 4 2 straight p subscript straight o straight V subscript straight o end style end fraction
equals space fraction numerator 1 over denominator 6.5 end fraction space equals space 15.4 percent sign