Solution Found!
Using Specific Volume, Volume, and PressureWarm air is
Chapter 1, Problem 42P(choose chapter or problem)
Warm air is contained in a piston-cylinder assembly oriented horizontally as shown in Fig. P1.42. The air cools slowly from an initial volume of \(0.003 \mathrm{~m}^3\) to a final volume of \(0.002 \mathrm{~m}^3\). During the process, the spring exerts a force that varies linearly from an initial value of \(900 \mathrm{~N}\) to a final value of zero. The atmospheric pressure is \(100 \mathrm{kPa}\), and the area of the piston face is \(0.018 \mathrm{~m}^2\). Friction between the piston and the cylinder wall can be neglected. For the air in the piston-cylinder assembly, determine the initial and final pressures, each in kPa and atm.
Questions & Answers
QUESTION:
Warm air is contained in a piston-cylinder assembly oriented horizontally as shown in Fig. P1.42. The air cools slowly from an initial volume of \(0.003 \mathrm{~m}^3\) to a final volume of \(0.002 \mathrm{~m}^3\). During the process, the spring exerts a force that varies linearly from an initial value of \(900 \mathrm{~N}\) to a final value of zero. The atmospheric pressure is \(100 \mathrm{kPa}\), and the area of the piston face is \(0.018 \mathrm{~m}^2\). Friction between the piston and the cylinder wall can be neglected. For the air in the piston-cylinder assembly, determine the initial and final pressures, each in kPa and atm.
ANSWER:
Solution 42P
Step 1 of 5
Here we have to calculate the initial and final pressure for the air in the given piston-cylinder assembly. In the given case, the air gets cooled slowly from the initial volume to a final volume
. In the process, the spring which is attached to piston, applies a spring force
which varies linearly from the initial value
to final value
. The area to the piston is given to be
and atmospheric pressure is
.
Given data,
Initial volume,
Final volume,
Initial spring force,
Final spring force, .
Piston area,
Atmospheric pressure,
To find,
Initial air pressure,
Final air pressure,