A tank of volume `0.2 m^3` contains helium gas at a temperature of `300 K` and pressure `1.0 xx 10^5 N m^(-2)`. Find the amount of heat required to raise the temperature to `400 K`. The molar heat capacity of helium at constant volume is `3.0 cal K^(-1 ) mol^(-1)`. Neglect any expansion in the volume of tank.

Explanation

The amount of the gas in moles is
`n=p^V/RT`
`=(1.0 xx 10^5 N m ^(-2)) (0.2 m ^3 )/(8.31 J K^(-1) mol^(-1)) (300 K )= 8.0mol`.
The amount of heat required is
`DeltaQ = nC_v Delta T`
`=(8.0 mol) (3.0 cal mol^(-1) K^(-1)) (100k ) 2400 cal`.