A dosed tank with a volume of 3.8 ft^3 is filled with nitrogen (N_2) at a temper

Question

A dosed tank with a volume of 3.8 ft^3 is filled with nitrogen (N_2) at a temperature of 552 degree R sitting at a pressure of 10 Ibf/in^2. Heat is added (2.3 Btu) to the tank as a fan stirs the nitrogen until a final temperature of 811 degree R. Determine for an ideal gas (using the tables in the back): The initial and final mass inside the tank in [lbm] The final pressure inside the tank in [lbf/in^2] The work done by the fun on the system in (Btu) while neglecting kinetic energy and potential energy effects. Now. recalculate pan (a) and part (b) assuming u real gas using the van der Waal* equation. Comment on the difference between the ideal gas and real gas results. Show all calculations and unit conversions otherwise no points will be given.

Explanation / Answer

Volume = 3.8 ft3 = 107.604 L

Initial temperature = 552 oR = 306.667 K

Final temperature = 811 oR = 450.556 K

Pressure = 10 lbf/in2 = 0.680 atm

(a). Using ideal gas equation:

PV = nRT

0.68 * 107.604 = n1 * 0.0821 * 306.667

n1 = 2.90

Againg using ideal gas equation with final temperature:

0.68 * 107.604 = n2 * 0.0821 * 450.556

n2 = 1.98

Molar mass of N2 = 28 g/mole

Initial mass = 2.9 * 28

= 81.2 grams

Final mass = 1.98 * 28

= 55.44 grams

(b). We know that:

P1 / n1T1 = P2/n2T2

0.68 / 2.9*306.67 = P2 / 1.98*450.55

P2 = 0.68*1.98*450.55 / 2.9*306.67

P2 = 0.682

= 10.024 lbf/in2

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