Question

5 moles of Nitrogen gas are enclosed in an adiabatic cylindrical vessel. The piston itself (which is free to move vertically) is a rigid, light cylindrical container, containing 3 moles of Helium gas, is placed over Nitrogen. There is a heater which gives out a power of 100 cal/s to the Nitrogen. A power of 30 cal/s is transferred to Helium through the bottom surface of the piston. The rate of increment of temperature of the nitrogen gas in $K/s$ is (assuming that the piston moves slowly and $R=2\frac{cal}{mol.K}$) (Answer upto two digits after the decimal)

Answer 1

Net power given to $N_2$ gas = 100 - 30 = 70 cal/s
The nitrogen gas expands isobarically as the pistion is free to move.
$Q=n{C}_{p}dT$
$\frac{dQ}{dt}=n{C}_p\frac{dT}{dt}$
$70=5\times \frac{7}{2}R\frac{dT}{dt}$
$R=2\frac{cal}{mol.K}$
$\therefore \frac{dT}{dt}=2K/sec$