Thermodynamics Hw help, piston designing

[Nilkc]

Homework Statement

Have a design project in thermodynamics. The problem reads,

Someone has suggested that the device shown in the figure below be used to improve the maximum force F against the spring, which has a spring constant of k. This is accomplished by changing the temperature of the liquid-vapor mixture in the container. You are to design such a device to close sun-blocking window-shutters that require a maximum force of 0.5 lbf. The piston must move 6 inches to close those shutters completely. You elect to use R-134a as the working fluid and arrange the liquid-vapor mixture container such that he temperature changes from 70 degrees F when shaded from the sun to 100 degrees F when exposed to the full sun. Select the sizes of the various components in this system to do this task. Also select the necessary spring constant and the amount of R-134a to be used.

Homework Equations

Force=pressure*Area
Force=k*x

The Attempt at a Solution

All of my work and all the info I have been using is in the attachments. I have been working it on a whiteboard at school. I can only load 3 pics. I continued on and found that the natural length of the spring is 9.707 inches with a k value of 0.031833 Lbf/in.

I am assuming that at 100 degrees F that the system is in equilibrium and the force to keep the windows closed is 0.5 lbf. The picture also shows the piston is closed off, so I am assuming that I don't need to worry about atmospheric pressure. I can't see where I am going wrong, but the piston diameter seems to small. Is this right or am I reading the original problem wrong.

 

[Nilkc]

Got it figured out.

 

[pjh0118]

I have assignment as what you did. So can you please give me your answer? so I can get some ideas. Please Help me.

 

[violinak]

Hi Nilkc, i have the same project and I'm having trouble with that, could you give me a hint?? hELP

 

[rezeew]

Dear student,

Thank you for your question. It appears that you have made good progress on your homework so far. However, I would like to point out a few things that may help you complete your design project.

Firstly, it is important to clearly define the problem and understand the objective. In this case, the objective is to design a device that can close sun-blocking window-shutters with a maximum force of 0.5 lbf. This means that the force exerted by the piston on the shutters should be at least 0.5 lbf.

Next, it is important to understand the role of temperature in this system. The temperature change from 70 degrees F to 100 degrees F is what will cause the liquid-vapor mixture to expand and exert a force on the piston. Therefore, the temperature difference is a key factor in determining the size and amount of R-134a needed for the system.

In your attempt at a solution, you have correctly identified the equations for force and have calculated the natural length and spring constant. However, your assumption that the force to keep the windows closed is 0.5 lbf at 100 degrees F is incorrect. The force needed to keep the windows closed will vary depending on the temperature and the size and weight of the shutters. Instead, the force to close the shutters should be 0.5 lbf, which means that the force exerted by the piston should be greater than this value.

To select the sizes of the various components in the system, you will need to use the equations you have identified and consider the force requirements, temperature change, and properties of R-134a. It may also be helpful to draw a free body diagram of the piston and consider the forces acting on it at different temperatures.

I hope this helps guide you in completing your design project. Good luck!