`5` moles of nitrogen gas are enclosed in an adiabatic cylindrical vessel. The piston itself is a rigid light cylindrical container containing `3` moles of helium gas. There is a heater which given out a power of `100` cal of which `30` cal is transferred to helium through the bottom surface of the piston. The rate of increment of temperature of the nitrogen gas assuming that the piston moves slowly is

Explanation

Net power given to `N_(2)` gas `=100-30=70` cal`//s`
The nitrogen gas expands isobarically.
`therefore Q=n Cp(dT)/(dt)` or `70=5xx(7)/(2)R(dT)/(dt)`
`therefore (dT)/(dt)=2k//`sec