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Solved: Using Energy Concepts and the Ideal Gas ModelOne
Chapter 3, Problem 139P(choose chapter or problem)
One kilogram of air in a piston-cylinder assembly undergoes two processes in series from an initial state where \(p_1=0.5 \mathrm{MPa}, T_1=227^{\circ} \mathrm{C}\) :
Process 1-2: Constant-temperature expansion until the volume is twice the initial volume.
Process 2-3: Constant-volume heating until the pressure is again \(0.5 \mathrm{MPa}\).
Sketch the two processes in series on a p-v diagram. Assuming ideal gas behavior, determine (a) the pressure at state 2, in MPa, (b) the temperature at state 3 , in \({ }^{\circ} \mathrm{C}\), and for each of the processes (c) the work and heat transfer, each in kJ.
Questions & Answers
QUESTION:
One kilogram of air in a piston-cylinder assembly undergoes two processes in series from an initial state where \(p_1=0.5 \mathrm{MPa}, T_1=227^{\circ} \mathrm{C}\) :
Process 1-2: Constant-temperature expansion until the volume is twice the initial volume.
Process 2-3: Constant-volume heating until the pressure is again \(0.5 \mathrm{MPa}\).
Sketch the two processes in series on a p-v diagram. Assuming ideal gas behavior, determine (a) the pressure at state 2, in MPa, (b) the temperature at state 3 , in \({ }^{\circ} \mathrm{C}\), and for each of the processes (c) the work and heat transfer, each in kJ.
ANSWER:Step 1 of 3
Part a
We are required to calculate the pressure at state 2.
The process can be shown as below.
This is an adiabatic process and the relation holds good.
For air,
Given data:
MPa
C =
K
From the relation , we can calculate
.
MPa
MPa
Therefore, the pressure at state 2 is 0.19 MPa.