4 30 points A rigid tank that is initially evacuated is conn

4 (30 points). A rigid tank that is initially evacuated is connected through a valve toa supply line that carries helium at 1 MPa and 300 K. Now the valve is opened, and helium is allowed to flow slowly intothe tank until the pressure reaches IMPa P2). The final temperature and mass of the helium gas in the tank are: T2 300 K and m2 1 kg. Determine the direction (Is heat transferred to or from the tank?) and amount of heat transfer in the process. Neglect kinetic and potential energies. (Treat helium as an ideal gas with constant specific heats and assume u = 0 at 0 K)

Solution

As Given ,

P1 = P2 = 1 MPa

T1 = T2 = 300 K

This is a isothermic process.

so, change in internal energ = 0

Q = -W

Work done W = P*[Vtank - (Vi + Vtank)]

W = P*Vi (where Vi = specific volume)

Specific volume from superheated table at 1 MPa and 300 K,

Vi = 0.000623 m^3/kg

W = 1*10^6*0.000623

W = 623.07 kJ/kg

Q = -623.07 kJ/kg

Heat is transferred fro the tank.