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)3/2R` and `C_(p)= 5/2R`
Work done by the gas in one complete cycle
`W= area ABCDA=P_(0)V_(0)` (figure)
From A to B, heat given to gas `= nC_(v)DeltaT`
`=1xx(5/2R) DeltaT= 5/2 (2P_(0)) Delta V= 5P_(0)V_(0)`
From C to D and from D to A, heat is rejected by the gas,
`Efficiency= ("work done by the gas"//"cycle")/("total heat given to gas"//"cycle")`
`=(P_(0)V_(0))/(3/2P_(0)V_(0)+5P_(0)V_(0))=2/(13)xx100= 15.4%`