An initially evacuated tank is to be filled with N2 gas from a supply line. The N2 gas in the supply line is at 20oC and 800 kPa. The volume of the tank is 0.5 m3, and the tank is to be filled until the pressure in the tank is 750 kPa. Determine the amount of N2 that flows into the tank, and the final temperature of the N2 in the tank, assuming that the tank is insulated.

Question

State i: Inlet (Supply Line); State 1: Initial State; State 2: Final State
Given: N2; Ti = 20oC; Pi = 800 kPa; V = 0.5 m3; P2 = 750 kPa;
Assume: P1 = 0; m1 = 0 (initially evacuated); Q = 0 (insulated). Also, as no information is given and these terms are unlikely to be significant, W = 0, and kinetic and potential energy can be neglected. No flow out of the tank.
N2 is an ideal gas with variable specific heats.

Answer 1

Solution: With the assumptions given employed, the general First Law can be reduced to
mihi = m2u2
From the conservation of mass, mi = m2
So, hi = u2
At Ti = 20oC, hi = 304.2 kJ/kg
Finding the temperature for state 2 that gives u2 = 304.2 kJ/kg yields T2 = 137oC = 410 K
From the ideal gas law, mi = m2 =P2V2 / RT2 = 3.08kg
where R = 0.297 kJ/kg-K