An insulated tank initially contains 1.25 kg N2 gas at 150 kPa and 25oC. The tank is to receive 3.0 kg of N2 gas from a supply line with N2 at 20oC. Determine the final temperature and pressure of the N2 in the tank.

Question

State i: Inlet (Supply Line); State 1: Initial State; State 2: Final State
Given: N2; Ti = 20oC; P1 = 150 kPa; T1 = 25oC = 298 K; m1 = 1.25 kg; mi = 3.0 kg; P2 =600 kPa;
Assume: 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. V = constant .
N2 is an ideal gas with variable specific heats.
What will be an ideal response?

Answer 1

Solution: With the assumptions given employed, the general First Law can be reduced to
mihi = m2u2 - m1u1
From the conservation of mass, mi = m2 - m1
At Ti = 20oC, hi = 304.2 kJ/kg
At T1 = 25oC, u1 = 221.07 kJ/kg
From the conservation of mass, m2 = 4.25 kg
Solving the First Law for u2 = 279.75 kJ/kg
Finding the temperature for state 2 that gives u2 = 304.2 kJ/kg yields T2 = 377 K = 104oC
From the ideal gas law: V = m1RT1/P1 = 0.738 m3
where R = 0.297 kJ/kg-K
P2 = m2RT2/V = 645 kPa

Note: If the tank had been initially empty, the final temperature would have been independent of whatever amount of gas had been added. But, the initial mass impacts the final temperature calculation, so one must either know how much mass was added, or the final pressure.