A Vessel contains helium, which expands at constant pressure when 15 kJ of heat is supplied to it. What will be the variation of the internal energy of the gas? What is the work performed in the expansion?

Answer

6

Explanation

Here `Delta Q = 15000 J` (given)
In an isobaric process, `Delta Q =C ""_(Delta T) , Delta U = C_V Delta T` (always)
`Delta W = (C_p - C_V ) Delta t = R Delta T` ( from ` Delta Q = Delta U + Delta W` relation )
But `C_p = (gamma R)/(gamma -1)` and `C_V = R/(gamma -1)" ":. Delta Q : Delta U : Delta W = (gamma R)/(gamma -1):R/(gamma - 1) : R = gamma =1:gamma - 1`
Helium is monoatomic, hence its `gamma = 5//3 " ":. Delta Q : Delta U : Delta W = 5/3 : 1:2/3 :5:3:2`
`:.(Delta U)/(Delta Q) = 3/5` or `Delta U = 3/5 xx15 kJ = 9 kJ," ":. (Delta W)/(Delta Q) = 2/5"or "Delta W = 2/3 xx15kJ = 6 kJ`