Helium gas goes through a cycle ABCDA as shown in figure. Efficiency of this cycle is nearly _______ (Imagine He is an ideal gas)

Helium gas goes through a cycle ABCDA as shown in figure. Efficiency o

1.	Helium gas goes through a cycle ABCDA as shown in figure. Efficiency of this cycle is nearly _______ (Imagine He is an ideal gas)
Answer» `9.1%` `10.5%` `12.5%` `15.4%` Solution :Work done in complete cyclic = AREA under P-V graph (Cyclic process is clockwise so work is positive) `therefore` W=Area of ABCD =AB x BC `=(2P_0-P_0)xx(2V_0-V_0)` `therefore W=P_0V_0` …(1) For He gas, Specific heat at constant VOLUME `C_v=3/2R` and Specific heat at constant pressure `C_p=5/2R` Heat absorbed (along path AB) at constant volume , `(DeltaQ)_(AB)=muC_VDeltaT=3/2muR DeltaT` `=3/2xxDeltaP V_0 [because PV=muRT]` `=3/2(2P_0-P_0)V_0=3/2P_0V_0` Heat absorbed (along path BC ) at constant pressure, `(DeltaQ)_(BC)=muC_P DeltaT =5/2muR DeltaT` `=5/2 (2P_0)DeltaV[because MUR DeltaT=PV]` `=5/2(2P_0)(2V_0-V_0)` `=5/2(2P_0xxV_0)` `=5P_0V_0` Heat is not absorbed at path CD and DA, `therefore` Total heat absorbed `Q_1=3/2P_0V_0+5P_0V_0` `=13/2P_0V_0` ...(2) `therefore` Efficiency `eta=W/Q_1` `=(P_0V_0)/(13/2P_0V_0)` (`because` From eq.(1) and (2)) `=2/13xx100%` =15.38% `approx` 15.4%