Solution Found!
Using Energy Concepts and the Ideal Gas ModelAs
Chapter 3, Problem 134P(choose chapter or problem)
As shown in Fig. P3.134, a piston-cylinder assembly fitted with a paddle wheel contains air, initially at \(560^{\circ} \mathrm{R}, 18 \mathrm{lbf} / \mathrm{in}^2\), and a volume of \(0.29 \mathrm{ft}^3\). Energy in the amount of \(1.7 \mathrm{Btu}\) is transferred to the air by the paddle wheel. The piston moves smoothly in the cylinder, and heat transfer between the air and its surroundings can be ignored. Assuming ideal gas behavior by the air, determine its final temperature, in \({ }^{\circ} \mathrm{R}\).
Questions & Answers
QUESTION:
As shown in Fig. P3.134, a piston-cylinder assembly fitted with a paddle wheel contains air, initially at \(560^{\circ} \mathrm{R}, 18 \mathrm{lbf} / \mathrm{in}^2\), and a volume of \(0.29 \mathrm{ft}^3\). Energy in the amount of \(1.7 \mathrm{Btu}\) is transferred to the air by the paddle wheel. The piston moves smoothly in the cylinder, and heat transfer between the air and its surroundings can be ignored. Assuming ideal gas behavior by the air, determine its final temperature, in \({ }^{\circ} \mathrm{R}\).
ANSWER:
Step 1 of 2
We have to determine the final temperature of the air
The final temperature of the air can be determined by find the internal energy of the final temperature using energy balance equation.
Where,
mass of air in kg
Btu
and
are the internal energy of the air at 560 oR and final temperature T oF
The mass of air can be found using ideal gas equation
where,
lbf/ in2 = 2592 lbf/ft2
ft3
oR
ft
lbf/lbmol
oR
molecular weight of air = 28.97 lb/lbmol
Thus,
= 0.0252 lb