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Solved: Using Energy Concepts and the Ideal Gas ModelAir
Chapter 3, Problem 135P(choose chapter or problem)
Air is compressed in a piston-cylinder assembly from \(p_1= 10 \mathrm{lbf} / \mathrm{in}^2, T_1=500^{\circ} \mathrm{R}\) to a final volume of \(V_2=1 \mathrm{ft}^3\) in a process described by \(p v^{1.25}=\) constant. The mass of air is \(0.5 \mathrm{lb}\). Assuming ideal gas behavior and neglecting kinetic and potential energy effects, determine the work and the heat transfer, each in Btu, using (a) constant specific heats evaluated at \(500^{\circ} \mathrm{R}\), and (b) data from Table A-22E. Compare the results and discuss.
Questions & Answers
QUESTION:
Air is compressed in a piston-cylinder assembly from \(p_1= 10 \mathrm{lbf} / \mathrm{in}^2, T_1=500^{\circ} \mathrm{R}\) to a final volume of \(V_2=1 \mathrm{ft}^3\) in a process described by \(p v^{1.25}=\) constant. The mass of air is \(0.5 \mathrm{lb}\). Assuming ideal gas behavior and neglecting kinetic and potential energy effects, determine the work and the heat transfer, each in Btu, using (a) constant specific heats evaluated at \(500^{\circ} \mathrm{R}\), and (b) data from Table A-22E. Compare the results and discuss.
ANSWER:a.)
Step 1 of 3
We have to determine the work and the heat transfer, using constant specific heats evaluated at 500°R.
The work done in a process described by constant is given by the expression
( ideal gas
Where,
and
are the initial and final
temperature in oR
The final temperature can be calculated using the equation
The initial volume is given by
oR and
1,440 lbf/ft2
=
ft3
Hence,
= 872.21 oR
Thus,
= 51.03 Btu