A quantity of heat Q is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas is

Options

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

Answer

A

Explanation

Heat input at constant pressure, `Q=nC_(P).Deltat`
According to first law of thermodynamics
`nC_(p)Deltat = nC_(V)Deltat+DeltaW`
`therefore Delta W=nRDeltat`
`(DeltaW)/Q = (nRDeltaT)/(nC_(P)DeltaT) = (C_(P)-C_(V))/C_(P)=1- C_(P)/C_(V)`
`therefore (DeltaW)/Q = 1- 1/gamma = 1-3/5 = 2/5`