How Much Heat is Required to Vaporize Water in a Rigid Tank?

[outoftown]

Homework Statement

A rigid tank has a volume of 0.01m3. It initially contains saturated water at a temperature of 200°C and a quality of 0.4. The top of the tank contains a pressure-regulating valve that maintains the vapor at constant pressure. This system undergoes a process whereby it is heated until all the liquid vaporizes. How much head (in kJ) is required? You may assume that there is no pressure drop in the exit line.

Homework Equations

V = Vl + 0.4*(Vv-Vl)

The Attempt at a Solution

From the steam tables I could calculate ΔHi easily which came to 1628.43 kJ/kg
Next I calcualted the mass initial by also getting the specific volume from the steam tables.
That came out to be 0.194 kg. Now my problem is, I don't believe my mass remains constant, does it? I do have something flowing out the pressure valve, so that would reduce my mass. If so, can I just calculate mass final by taking specific volume final/actual volume? How do I know if my temperature remain constant in the system? I would think my temperature would drop from PV=nRT, but I don't know for sure.

Any help solving this would be greatly appreciated.

 

[KataKoniK]

Hello,

Thank you for your post. It seems like you have made some good progress in your attempt to solve this problem. Here are a few suggestions that may help you:

1. It is correct to assume that the mass in the tank will not remain constant. As the liquid vaporizes, its volume will increase and some of it will flow out of the tank through the pressure-regulating valve.

2. To calculate the final mass, you can use the ideal gas law, PV = nRT, where n is the number of moles. Since the pressure and temperature are constant in this process, you can rearrange the equation to get n = PV/RT. Then, you can use the specific volume to calculate the final mass, as you suggested.

3. In order to determine if the temperature remains constant, you can use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance to its temperature. This can help you determine if the temperature changes during the process.

I hope this helps. Let me know if you have any further questions or if you need clarification on any of these points. Good luck with your calculations!