Change in Entropy for Mixing of Two Liquids

In summary, the problem involves finding the change in entropy for one of the volumes of liquid in terms of initial temperature (T1) and the temperature after the two volumes of water mixed (T2). The equation to use is ΔS=∫(dQ/T) from state A to state B and it may be helpful to assume that the volume of the liquid does not change when mixed and cooled/heated.
  • #1
Alvin92SD
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Homework Statement


You mix 1 liter of water at 20°C with 1 liter of water at 80°C. Set up an equation to find the change in entropy for one of the volumes of liquid in terms of initial temperature (T1) and the temperature after the two volumes of water mixed (T2)


Homework Equations


ΔS=∫(dQ/T) from state A to state B



The Attempt at a Solution


Honestly I don't even know where to start or if I am using the right formula. I tried imagining a process where the volume of water is increased at constant temperature and then the temperature is increased from T1 to T2. I would be grateful if someone pointed me in the right direction.
 
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  • #2
This is a bit tricky problem; it would be much more clear if you were dealing with ideal gases instead. Now you just need to ignore the increase of entropy coming from the mixing of the two liquids.

Perhaps you can assume that the volume of the liquid does not change when it's mixed and cooled/heated. Then you can write
[tex]dS = \left(\frac{\partial S}{\partial T}\right)_V dT +\left(\frac{\partial S}{\partial V}\right)_T dV = C_V \frac{dT}{T} [/tex]
 

What is the definition of entropy?

Entropy is a measure of the disorder or randomness in a system. It is often referred to as the "degree of chaos" in a system.

What is the change in entropy for mixing of two liquids?

The change in entropy for mixing of two liquids is a measure of the increase in disorder when two different substances are mixed together. This can be calculated using the formula ΔS = −nR ln(X), where n is the number of moles of the substances, R is the gas constant, and X is the mole fraction of each substance in the mixture.

How does temperature affect the change in entropy for mixing of two liquids?

Temperature plays a significant role in the change in entropy for mixing of two liquids. As temperature increases, the change in entropy for mixing also increases. This is because at higher temperatures, the molecules have more kinetic energy and are more likely to move around and mix with each other, resulting in a greater increase in disorder.

What is the relationship between the change in entropy for mixing of two liquids and the spontaneity of the process?

The change in entropy for mixing of two liquids is closely related to the spontaneity of the process. In general, a positive change in entropy (ΔS > 0) indicates a spontaneous process, while a negative change in entropy (ΔS < 0) indicates a non-spontaneous process. The more positive the change in entropy, the more spontaneous the process will be.

Can the change in entropy for mixing of two liquids be negative?

Yes, the change in entropy for mixing of two liquids can be negative. This would indicate that the mixing process is non-spontaneous and would require an input of energy to occur. In most cases, however, the change in entropy for mixing is positive as mixing typically increases disorder and is therefore a spontaneous process.

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