# How Do You Relate Entropies to Temperatures in Water Mixing?

• gfd43tg
In summary, the conversation is about determining the difference in entropies, S1 and S2, in order to calculate the total entropy change for a system with two different masses. The suggested method is to use reversible processes to compute the entropy changes before and after reducing the temperatures of both solutions. The final step is to add the two entropy changes together to get the total change in entropy. It is important to note that this method does not require specific entropies.
gfd43tg
Gold Member

I don't know how to relate the entropies, S1 and S2, to the temperatures in my entropy balance

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Can't say I understand your attempt.

In order to determine entropy differences you have to come up with one or more reversible processes. Then you can compute the difference in entropies before & after.

Hint: take the hotter water solution and reversibly reduce its temperature from its original temperature to the final temperature of the two solutions. Compute ΔShotter.

Do the same for the cooler solution.

You wind up with two solutions of equal temperature, then you can mentally just pour them together without any further changes in any thermodynamic coordinate.

Answer will be ΔScooler - ΔShotter.

I am just doing an entropy balance on my control volume, being the tank where the two liquids are mixed. I just can't find an absolute value of entropy for S1 and S2

You never deal with absolute entropies in introductory physics. You deal in differences in entropy between two (or more) states.

So the hotter water's entropy changes by ΔSh and the colder by ΔSc. The total change in entropy is ΔSc + ΔSh.

I was able to solve it. The tricky thing at the end is to get it in the form they want, you have a squared term on top, so you have to take out a square from the top and bottom to make the bottom have the square root in it.

For the part with two masses being different, if I add them together, how can I get one expression for the total entropy? I can get the mass specific total entropy change, but not sure about the total entropy change.

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Maylis said:
I was able to solve it. The tricky thing at the end is to get it in the form they want, you have a squared term on top, so you have to take out a square from the top and bottom to make the bottom have the square root in it.

yes, I noticed that too.

For the part with two masses being different, if I add them together, how can I get one expression for the total entropy? I can get the mass specific total entropy change, but not sure about the total entropy change.
I don't know how exactly you did the math. If you did it the way I suggested it's a straightforward extension of the method. You compute the two entropy changes independently and then add them. You don't need specific entropies. Of course, the final temperature will not be the mean of the two starting temperatures.

Post your math if you want to.

EDIT Sorry, I hadn't noticed mass-specific heat of water already used in part (a). Of course, use it again for part (b). This is usually written with a lower-case c which is what threw me off in the originally provided answer.

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## What is the definition of entropy change of water mixing?

The entropy change of water mixing is a measure of the disorder or randomness of a system when two different bodies of water are mixed together. It takes into account the change in temperature, pressure, and volume of the system.

## How is the entropy change of water mixing calculated?

The entropy change of water mixing can be calculated using the formula ΔS = nRln(V2/V1), where ΔS is the change in entropy, n is the number of moles of water, R is the gas constant, and V1 and V2 are the initial and final volumes of the water.

## Does the entropy change of water mixing always increase?

Yes, the entropy change of water mixing always increases because the mixing of two bodies of water results in a more disordered or random system.

## How does the temperature affect the entropy change of water mixing?

The temperature has a significant effect on the entropy change of water mixing. As the temperature increases, the entropy change also increases. This is because at higher temperatures, the molecules of water have more energy and move around more, resulting in a more disordered system.

## Can the entropy change of water mixing be reversed?

Yes, the entropy change of water mixing can be reversed by applying energy in the form of heat or work to the system. This can result in the separated bodies of water returning to their initial state, with the same amount of disorder as before the mixing process.

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