## Ch 9 #1c Why does Entropy decrease when temperature increases?

andrea_Disc3D
Posts: 10
Joined: Wed Sep 21, 2016 2:55 pm

### Ch 9 #1c Why does Entropy decrease when temperature increases?

The question asks what happens to the entropy generated by your body heat when the temperature of the room increases from 20 degrees Celsius to 30 degrees Celsius.

I understand mathematically why entropy decreases because the denominator (Temperature) in the entropy equation deltaS=q/t increases and since the number you are dividing by a bigger number, your answer (Entropy) is smaller. However, I don't get how this is logically true because intuitively I would expect entropy to increase because increase in temperature causes molecules to move more and increase in randomness.

Maggie Bui 1H
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Joined: Fri Jul 22, 2016 3:00 am
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### Re: Ch 9 #1c Why does Entropy decrease when temperature increases?

As you said, mathematically, this makes sense; if you calculate the entropy change with some q value at 20 degrees Celsius and the same q value at 30 degrees Celsius, the entropy change of the 2nd calculation is smaller than that of the first.

Rather than the temperature change though, I think it's important to notice that q is not changing in this problem; that is, the energy added to the system as heat is not changing. In light of this, the statement might make more sense. We're adding the same amount of heat (q) at different temperatures. That same amount of heat would increase entropy more at a lower temperature than at a higher one. It's like throwing a rock into a swimming pool versus throwing a rock into the ocean - by the virtue of the environment, the same action causes more change in one scenario than it does in the other.

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