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)

Options

A. `15.4%`
B. `9.1%`
C. `10.5%`
D. `12.5%`

Answer

A

Explanation

Helium is monoatomic gas, for which `C_(V)= (3)/(2)R, C_(P)= (5)/(2)R`
Work done by the gas in one complete cycle W= area `ABCDA= p_(0)V_(0)`
From A to B, Heat given to gas `=nC_(V) Delta T= 1 xx ((3)/(2) R) xx Delta T= (3)/(2) V_(0) (Delta p)= (3)/(2) V_(0)p_(0)`
From B to C, heat given to gas `=nC_(P) Delta T =1 xx ((5)/(2)R) xx Delta T= (5)/(2) (2p_(0)) Delta V= 5p_(0)V_(0)`
Efficiency of cycle `=("Work done by the gas/cycle")/("Total heat given to gas/cycle")`
`=(p_(0)V_(0))/((3)/(2) p_(0)V_(0) + 5p_(0)V_(0))= (2)/(13)`
Efficiency (%) `=(2)/(3) xx 100= 15.4 %`