Helium gas goes through a cycle $ABCDA$ ( consisting of two isochoric and isobaric lines) as shown in figure Efficiency of this cycle is nearly ....... $\%$ (Assume the gas to be close to ideal gas)
AIEEE 2012, Diffcult
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$Heat\,given\,to\,system = {\left( {n{C_V}\Delta T} \right)_{A \to B}} + {\left( {n{C_p}\Delta T} \right)_{B \to C}}$
$ = {\left[ {\frac{3}{2}\left( {nR\Delta T} \right)} \right]_{A \to B}} + {\left[ {\frac{5}{2}\left( {nR\Delta T} \right)} \right]_{B \to C}}$
$ = {\left[ {\frac{3}{2} \times {V_0}\Delta p} \right]_{A \to B}} + \left[ {\frac{5}{2} \times 2{P_0} \times {V_0}} \right]$
$ = \frac{{13}}{2}{P_0}{V_0}$
$and\,\,{W_0} = {P_0}{V_0}$
$\eta = \frac{{Work}}{{heat\,given}} = \frac{{{P_0}{V_0}}}{{\frac{{13}}{2}{P_0}{V_0}}} \times 100 = 15.4\% $
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