The volume (V) of a monoatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is ____

Options

A. `2/7`
B. `2/5`
C. `1/3`
D. `2/3`

Answer

B

Explanation

`V prop T`
In isobaric process `W=PDeltaV=muR DeltaT` ….(1)
`DeltaQ=mu C_P DeltaT`…(2)
For monatomic gas molecule f=3
`therefore C_P=f/2 R +R =5/2 R` …(3)
`[because f=3]`
`therefore W/(DeltaQ)=(muR DeltaT)/(mu C_P DeltaT)` [From equ. (1) and (2)]
`therefore W/(DeltaQ)=R/C_P=R/(5/2R)` [From equ. (3)]
`therefore W/(DeltaQ)=2/5`