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Old Feb 9th 2018, 08:41 AM   #1
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The entropy change of solids and incompressible liquids

This was asked as an addendum to another thread so I have started it as a new thread.

Originally Posted by casperneo View Post
I have another question regarding thermodynamics,

A ship's anchor, made of 500kg of steel and initially at a temperature of 20 degree is dropped into the ocean which has a temperature of 7 degree. Determine the entropy change of the anchor.

Can i assume that since the ocean has a huge volume, the ocean water would not change temperature. Thus, the steel anchor will have a final temperature of 7 degree.

Solving it, using Cp= 4.002KJ/KG.K
The answer is -0.18162 KJ/K.
I'm sorry but this is not correct since the temperature of the anchor varies during the cooling.

In any case you should have started a new thread for this.
I will do this for you and we can continue the discussion there.


For incompressible substances dv = 0 so combining the first law and the definition of the second law entropy

In differential form

ds = du/T = Cdt/T

So for a temperature change from T1 to T2

The entropy change S2 - S1 =[ Integral CdT/T ] from T1 to T2

If we can take the specific heat as constant then

S2 - S1 = C ln T2/T1, after performing the integration.

I think this is a bit above high school level though.
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Old Feb 9th 2018, 09:07 AM   #2
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Originally Posted by studiot View Post
In differential form

ds = du/T = Cdt/T

So for a temperature change from T1 to T2

The entropy change S2 - S1 =[ Integral CdT/T ] from T1 to T2

If we can take the specific heat as constant then

S2 - S1 = C ln T2/T1, after performing the integration.

I think this is a bit above high school level though.
Yes... this question is a typical question you'd get as a first-year undergraduate in a physics degree. However, the integration is nothing special and a final-year high school student should be able to solve it if they've been taught about entropy properly. Therefore, it wouldn't be particularly onerous for a student if it appeared in a final-year high school syllabus.
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