An initially evacuated tank is to be filled with CO2 gas from a supply line which contains CO2 at 150 psia and 70oF. The tank volume is 10 gal, and the tank is to be filled until the pressure inside the tank is 120 psia. Determine the amount of heat transfer required if the temperature of the CO2 in the tank is to be 80oF.
State i: Inlet (Supply Line); State 1: Initial State; State 2: Final State
Given: CO2; Ti = 70oF; Pi = 150 psia; V = 10 gal = 1.34 ft3; P2 = 120 psia; T2 = 80oF
Assume: P1 = 0; m1 = 0 (initially evacuated). 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. CO2 is an ideal gas with variable specific heats.
Solution: With the assumptions given employed, the general First Law can be reduced to
Q + mihi = m2u2
From the conservation of mass, mi = m2
At Ti = 70oF, hi = 90.17 Btu/lbm
At T2 = 80oF, u2 = 67.81 Btu/lbm
From the ideal gas law, mi = m2 = P2V2 / RT2 = 1.22 lbm
where R = 35.11 ft-lbf/lbm-R, and T = 540 R.
Solving for the heat transfer yields Q = -27.3 Btu .
Note: As the CO2 will heat as it enters and stops in the tank, heat must be removed to cool the O2 to 80oF.
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