## Temperature Relation

$\Delta U=q+w$

Cristina Sarmiento 1E
Posts: 52
Joined: Wed Nov 16, 2016 3:02 am

### Temperature Relation

Can someone please explain the relationship between temperature and internal energy ?
Also, the relationship between temperature and entropy?
Thanks

Cooper1C
Posts: 50
Joined: Fri Sep 29, 2017 7:07 am

### Re: Temperature Relation

Relationship between T and delta U:

$\Delta U = q$ (assuming no work is done)

If you increase heat added (increase q) then delta U increases.

Relationship between T and delta S:

delta S$\Delta S __{T_{1} \rightarrow T_{2}} = nC(\ln T_{2} - \ln T_{1})$

If you look at the natural log graph:

If $T_{2}> T_{1}$ ($\Delta T> 0$), $\ln T_{2} - \ln T_{1}$ is positive and $\Delta S$ is positive.
If $T_{2}> T_{1}$ ($\Delta T< 0$), $\ln T_{2} - \ln T_{1}$ is negative and $\Delta S$ is negative.

Andrew Nguyen 2I
Posts: 68
Joined: Fri Sep 29, 2017 7:07 am

### Re: Temperature Relation

Also the internal energy of an ideal gas is determined by the temperature so if there's no change in temperature there can be no change in internal energy for the gas.