Thermo - mixing water in a container.

[Thyferra2680]

A partition separates the two compartments of a vessel. The vessel is submerged in a constant temperature bath at 200C. Compartment A contains 2.00 kg of water at 200C, 50.00 bar and compartment B contains 0.983 kg of water at 200C, 1.00 bar. The partition is removed and the water in both compartments fills up the entire vessel. Determine the final pressure, and the heat transfer that results from the mixing process, if the final temperature
is 200C.

I'm working on a practice test for my thermoclass, and I've been stuck on this problem for a while... What I've tried so far...

Since this is water, I assumed that you could use density and just say that the volume of the compartments A and B are 2 m^3 and .983 m^3 respectively. I first assumed that it would have something to do with work, but W = PV isn't valid here because this isn't a gas. I'm trying Enthalpy changes, but I'm not given an internal energy for the equation H = U + PV. I am however given several charts, Saturated Steam Tables for temperature and pressure, and a table of Superheated Steam properties.

So I guess I don't really know how to start finding the Pressure. Any hints to lead me to that?

 

[Q_Goest]

Hi Thyferra,
Here's an outline of the solution:

Let's consider the control volume to be the sum of the two volumes. There's a partition in the middle of this control volume. When that partition is removed, there is no work being done by this control volume, so dU = 0.

Can you determine the internal energy in each of the two sections? m u = U so use the steam tables to determine u and multiply by m to find U. The total internal energy (U₁ + U₂) for the entire volume after the partition is removed does not change, so now you can find u from the same equation: u = (U₁ + U₂) / (m₁ + m₂).

Now, from the steam tables, you should be able to locate the state of the water given u and density. That state is completely defined by those two variables, so you should be able to look up the temperature and pressure from that state. The temperature is assumed to be something other than 200 C.

Once you have the state after removal of the partition, you need to determine how much heat is required to raise/lower the temperature to 200 C. Application of the first law gives dU = Q or U_f - U_i = Q. You have U_i so you need U_f to determine Q.

You can find U_f using your steam tables because you know certain things about the final state, you know temperature and density. From temperature and density, you can find the state and thus find u_f. Therefore, you can calulate U_f = u_f m_f

Hope that helps.

 

[thomate1]

I would approach this problem by first understanding the physical properties of water and how they change with temperature and pressure. From the given information, it is clear that the water in both compartments is at the same temperature and is submerged in a constant temperature bath at 200C. Additionally, the partition separating the two compartments is removed, allowing the water to mix and fill the entire vessel.

To determine the final pressure, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume. However, since water is not a gas, we cannot use this equation directly.

Instead, we can use the concept of partial pressures. When the partition is removed, the water molecules in compartment A will mix with those in compartment B, creating a mixture of water at the same temperature. The total pressure of this mixture will be the sum of the partial pressures of each compartment.

Using the ideal gas law, we can calculate the partial pressures of each compartment before the partition is removed. For compartment A, the pressure is 50.00 bar, and for compartment B, the pressure is 1.00 bar. Therefore, the total pressure of the mixture will be 51.00 bar.

To calculate the heat transfer that results from the mixing process, we can use the concept of enthalpy. Enthalpy is a measure of the total energy of a system, including both its internal energy and the work done on or by the system. In this case, the enthalpy change will be equal to the heat transfer that occurs during the mixing process.

To calculate the enthalpy change, we can use the equation H = U + PV, where H is the enthalpy, U is the internal energy, P is the pressure, and V is the volume. Since the temperature remains constant at 200C, the internal energy will also remain constant. Therefore, the enthalpy change will be equal to the work done by the system, which can be calculated using the formula W = PΔV.

Using the calculated total pressure of 51.00 bar and the known initial volumes of compartments A and B, we can calculate the change in volume when the water mixes. This will give us the work done by the system, which is equal to the heat transfer that occurs during the mixing process.

In conclusion, the final pressure in the vessel after mixing will be 51.00