Hydrogen gas is contained in a vertical piston-cylinder device at 14.7 psia and

Question

Hydrogen gas is contained in a vertical piston-cylinder device at 14.7 psia and 15 ft3.At this state, a linear spring with a spring constant of 12,000 lbf/ft touches the top of the piston but exerts no force on it. The cross-sectional area of the piston is 2.5 ft2. Heat transfer occurs to hydrogen gas, pushing the piston upwards against the spring, and the hydrogen gas expands until its volume doubles.

(a) Show the process on a p-V diagram.
(b) Determine final pressure (psia) of the hydrogen gas.
(c) What is the total work done (Btu) during the expansion process?
(d) What fraction of the above work (Btu) is done against the spring?

Explanation / Answer

The key to determining the final pressure is that initially the spring is touching the piston, but exerting no force. So, as the H2 gas expands, the pressure in the cylinder increases because the spring pushes on the back of the piston. As a result: P2 = P1 + Fspring/Apiston = P1 + ksp*dx/Apiston Where dx if the distance by which the spring is compressed during the expansion. dx = (V2-V1)/Apiston = (30 ft3 - 15 ft3) / 2.5 ft2 = 6ft Plugging in numbers: P2 = 14.7 psia + (12,000 lbf/ft * 6 ft / 2.5 ft2)/144 in2/ft2 = 214.7 psia Expansion work is done to overcome the external ambient pressure of 14.7 psia (Wambient) and also to overcome the resistance of the spring (Wspring). Wambient = Pambient *(V2-V1) = 14.7 psia * 144 in2/ft2 * ( 30ft3 - 15 ft3) Wambient = 31752 ft-lbf / 778.3 ft-lbf/Btu = 40.8 Btu Because the spring is LINEAR, the process path on a PV diagram is also linear. The total work is the area under this linear process path and that is just the average pressure multiplied by the change in volume. Wtotal = [(P1+P2)/2]*(V2-V1) Wtotal = [(14.7 psia+214.7 psia)*144 in2/ft2 / 2] * (30 ft3 - 15 ft3) Wtotal = 247752 ft-lbf / 778.3 ft-lbf/Btu = 318.32 Btu The spring work is the difference between the total work and work done against ambient pressure. Wspring = Wtotal - Wambient = 281.7 - 40.8 = 240.9 Btu Finally, the fraction of the work done agaiunst the spring is: fraction = Wspring / Wtotal = 240.9 / 281.7 = 85.5%

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.