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.

Answer

`[2400 cal.]`

Explanation

For monoatomic gas `C_(v)=(3)/(2)R, n_(1)=1 mol e`
For diatomic gas, `C_(v)=(5)/(2)R, n_(2)=3 mol e`
Average molar specific heat of mmixture at constant volume is,
`C_(v)=(n_(1)(C_(v))_(1)+n_(2)(C_(v))_(2))/(n_(1)+n_(2))=(1xx(3)/(2)R+3xx(5)/(2)R)/((1+3))`
`C_(v)=(9)/(4)xx8.31xx300=8 mol e`
`:.` Amount of heat requuired
`Delta Q=nC_(v) Delta T=8xx3.0xx(400-300)`
`Delta Q=2400 cal`