A sample of ideal gas `(gamma = 1.4)` is heated at constant pressure. If 100 J of heat is supplied to the gas the work done by the gas is

Options

A. 28.57 J
B. 56.54 J
C. 38.92 J
D. 65.38 J

Answer

A

Explanation

At constant pressure,
`Delta Q = nC_(P) Delta T` and `Delta U = nC_(V) Delta T`
From the first law of thermodynamics,
`Delta W = Delta Q - Delta U = n(C_(P) - C_(V)) Delta T`
`:. (Delta W)/(Delta Q) = (n(C_(P) - C_(V))Delta T)/(nC_(P)Delta T) = 1 - (C_(V))/(C_(P)) = 1-(1)/(gamma)`
`= 1-(1)/(1.4) = (0.4)/(1.4) = (4)/(14) = (2)/(7)`
or `Delta W = (2)/(7) Delta Q = (2)/(7) xx 100 J = 28.57 J`