Solution Found!
Applying the Energy BalanceFigure P3.83 shows a
Chapter 3, Problem 83P(choose chapter or problem)
Figure P3.83 shows a piston-cylinder assembly fitted with a spring. The cylinder contains water, initially at \(1000^{\circ} \mathrm{F}\), and the spring is in a vacuum. The piston face, which has an area of \(20 \mathrm{in}^2\), is initially at \(\mathrm{x}_1=20 \mathrm{in}\). The water is cooled until the piston face is at \(\mathrm{x}_2=16 \mathrm{in}\). The force exerted by the spring varies linearly with x according to \(F_{\text {spring }}=\mathrm{kx}\), where \(\mathrm{k}=200 \mathrm{lbf} / \mathrm{in}\). Friction between the piston and cylinder is negligible. For the water, determine
(a) the initial and final pressures, each in \(\mathrm{lbf} / \mathrm{in}^2{ }^2\)
(b) the amount of water present, in lb.
(c) the work, in Btu.
(d) the heat transfer, in Btu.
Questions & Answers
QUESTION:
Figure P3.83 shows a piston-cylinder assembly fitted with a spring. The cylinder contains water, initially at \(1000^{\circ} \mathrm{F}\), and the spring is in a vacuum. The piston face, which has an area of \(20 \mathrm{in}^2\), is initially at \(\mathrm{x}_1=20 \mathrm{in}\). The water is cooled until the piston face is at \(\mathrm{x}_2=16 \mathrm{in}\). The force exerted by the spring varies linearly with x according to \(F_{\text {spring }}=\mathrm{kx}\), where \(\mathrm{k}=200 \mathrm{lbf} / \mathrm{in}\). Friction between the piston and cylinder is negligible. For the water, determine
(a) the initial and final pressures, each in \(\mathrm{lbf} / \mathrm{in}^2{ }^2\)
(b) the amount of water present, in lb.
(c) the work, in Btu.
(d) the heat transfer, in Btu.
ANSWER:
Part (a)
Step 1 of 9:
Consider water contained cylinder with a piston. The spring is in a vacuum. The water is cooled down to a particular temperature. The piston moves as the water cool down. The force exerted by the spring is directly proportional to the distance moved. The effects of frictional force can be neglected. We are going to find the initial and final pressure in lbf/in2.
The initial temperature T1 = 1000°F
The area of the piston face A = 20 in2
The initial distance x1 = 20 in
The final distance x2 = 16 in
The spring constant k = 200 lbf/in