Thermo I Question: Two vessels coming to equilibrium. Finding final values.

In summary, the problem involves two rigid vessels connected by a valve and tubing, filled with water at different pressures and temperatures. To solve, the total mass of water, initial average specific volume, and initial internal energy are determined. Using steam tables, the final equilibrium pressure and amount of heat transfer can be calculated when the system reaches thermal equilibrium with the surroundings at 50˚C. The continuity equations and steam tables are used, and hints may be needed to solve the problem.
  • #1
deltagal
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Hey, guys. I am currently in a Thermo I class and have ran into a problem that has me completely stumped. I have worked in numerous different ways and anything I come up with doesn't seem to make since or be realistic. Here's the question:

Two rigid vessels are connected by a small valve and tubing. Both are of negligible size. Vessel 1 contains .8m3 of water at 650kPa at a quality of 50%. Vessel 2 contains .4m3 of water at 400kPa and 250ºC. If the valve is oped and both vessels come to equilibrium, determine the final equilibrium pressure and the amount of heat transfer when the system reaches thermal equilibrium with he surroundings which are at 50˚C.

I have currently been using the continuity equations and using steam tables to get the values that I need. My Prof said I was on the right track but wasn't very helpful at all during our session. I hope you guys can give me some hints. Thanks.
 
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  • #2
Step 1: Determine the total mass of water in the two tanks
Step 2: Determine the initial average specific volume = (total volume of tanks)/(total mass of water)
Step 3: Determine the initial internal energy in the two tanks
Step 4: Find the final state of the system for water at 50 C and the same average specific volume as initially to get the final pressure
Step 5: Determine the final internal energy
Step 6: Determine the change in internal energy
Step 7: The heat transfer is equal to the change in specific volume
 

Related to Thermo I Question: Two vessels coming to equilibrium. Finding final values.

1. How do the initial temperatures affect the final equilibrium temperature?

The initial temperatures of the two vessels play a key role in determining the final equilibrium temperature. If the initial temperatures are significantly different, the final temperature will likely be closer to the initial temperature of the vessel with the higher initial temperature. If the initial temperatures are close, the final temperature will be closer to the average of the two initial temperatures.

2. What factors can affect the rate at which the two vessels come to equilibrium?

The rate at which the two vessels come to equilibrium is affected by several factors, including the temperature difference between the two vessels, the heat transfer coefficient of the vessels, and the thermal conductivity of the material in the vessels.

3. How can we calculate the final equilibrium temperature?

To calculate the final equilibrium temperature, we can use the heat transfer equation, which takes into account the initial temperatures of the two vessels, their heat transfer coefficients, and the thermal conductivity of the material. We can also use the concept of energy balance, where the total energy lost by one vessel is equal to the total energy gained by the other vessel at equilibrium.

4. What happens to the temperature of the vessels if they have different thermal conductivities?

If the two vessels have different thermal conductivities, the final equilibrium temperature will be closer to the initial temperature of the vessel with the higher thermal conductivity. This is because the vessel with the higher thermal conductivity will be able to transfer heat more quickly, resulting in a higher final temperature.

5. Can the final equilibrium temperature be lower than both initial temperatures?

Yes, it is possible for the final equilibrium temperature to be lower than both initial temperatures. This can happen if one vessel has a significantly higher heat transfer coefficient or thermal conductivity, allowing it to transfer more heat to the other vessel. In this case, the final temperature will be closer to the initial temperature of the vessel with the lower thermal properties.

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