Calculate entropy difference

In summary, to compute the entropy difference between 12 kg of water at 40°C and 12kg of ice at -10°C, you can use the standard entropy of water at 298K as the baseline. Calculate the change in entropy to go from water at 298K to 0°C, then from 0°C to -10°C, including the heat of melting of ice. Next, calculate the change in entropy to go from 298K to 40°C. Finally, subtract the two values to find the entropy difference. The mass of the water will not affect the result since it remains constant.
  • #1
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Homework Statement


Compute the entropy difference between 12 kg of water at 40°C and 12kg of ice at -10°C.
Cp,water=4.184 J/g.K
Cp,ice=2.1 J/g.K
Heat of melting of ice=336 kJ/kg
Standard entropy of water at 298K = 69.9 J/K.mol


Homework Equations



S=the integral of cp/TdT

The Attempt at a Solution



I broke it down into different phases, the first one being delta S from -10 to 0, then from 0 to 40 degrees. Then I will add the heat of melting to the total entropy. Mass should be irrelevant since it remains constant. My problem is what to do with the standard entropy of water. Am I supposed to add it to my entropy equaiton as well?
 
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  • #2
"My problem is what to do with the standard entropy of water. Am I supposed to add it to my entropy equaiton as well?"

Why not use it as the basic datum point for the whole problem? Compute the change in entropy to go from water at 298K or 25C to 0, then phase change, then to -10C. Then compute the change in entropy to go from 25C to 40C. Now you will have the difference when you compare the two values.
 

1. What is entropy and why is it important to calculate the difference?

Entropy is a measure of the disorder or randomness in a system. It is important to calculate the difference in entropy because it can provide insight into the energy and information flow within a system.

2. How is the entropy difference calculated?

The entropy difference is calculated by subtracting the initial entropy value from the final entropy value. This can be done using the formula ΔS = Sfinal - Sinitial.

3. What factors can affect the entropy difference?

The entropy difference can be affected by changes in temperature, pressure, and the number of particles in a system. It can also be influenced by chemical reactions and phase changes.

4. Can the entropy difference ever be negative?

Yes, the entropy difference can be negative. This indicates a decrease in disorder or randomness within the system. However, this is only possible if there is an external source of energy that is driving the decrease in entropy.

5. How is the entropy difference used in scientific research?

The concept of entropy difference is used in various fields of science, such as thermodynamics, chemistry, and information theory. It can be used to predict and analyze the behavior of systems, as well as to determine the direction and spontaneity of chemical reactions.

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