# Change of Entropy question

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#1

1. Show that the change of entropy delta S in a metal block of mass m and specific heat capacity C subjected to a change in temperature from T1 to T2 is 􏰂delta S 􏰁=mCloge(T2 /T1 ).

Very stuck, I've looked up books and the internet and tried to work backwards but have no idea why there's a loge (the e is a small e). The closest idea I got was the ideal thermodynamic efficiency n = 1-T2/T1 which kind of looks like the (T2/T1) in the equation of the question. How do I even start this?
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3 years ago
#2
(Original post by Airess3)
1. Show that the change of entropy delta S in a metal block of mass m and specific heat capacity C subjected to a change in temperature from T1 to T2 is 􏰂delta S 􏰁=mCloge(T2 /T1 ).

Very stuck, I've looked up books and the internet and tried to work backwards but have no idea why there's a loge (the e is a small e). The closest idea I got was the ideal thermodynamic efficiency n = 1-T2/T1 which kind of looks like the (T2/T1) in the equation of the question. How do I even start this?
You need to start from the "definition" of infinitesimal entropy change
dS during an infinitesimal reversible process at absolute temperature T

loge is natural log.

Spoiler:
Show

This problem is found in the physics textbook that you have. It is a solved example in chapter 20.

0
3 years ago
#3
(Original post by Airess3)
1. Show that the change of entropy delta S in a metal block of mass m and specific heat capacity C subjected to a change in temperature from T1 to T2 is 􏰂delta S 􏰁=mCloge(T2 /T1 ).

Very stuck, I've looked up books and the internet and tried to work backwards but have no idea why there's a loge (the e is a small e). The closest idea I got was the ideal thermodynamic efficiency n = 1-T2/T1 which kind of looks like the (T2/T1) in the equation of the question. How do I even start this?

So the energy needed to heat a block of mass m, with specific heat capacity C by an amount dT is

thus we have that

I'll leave you to do the integral
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