Is there a name for this sort of thermo relationship? H_(vap sub cond)(T')-H_(vap sub cond)(T)= int_(T)^(T')Delta C_(p,m)dT

capellitad9 2022-07-19 Answered
Is there a name for this sort of thermo relationship?
H v a p / s u b / c o n d ( T ) H v a p / s u b / c o n d ( T ) = T T Δ C p , m d T
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Answers (1)

hottchevymanzm
Answered 2022-07-20 Author has 15 answers
The relation arises from integrating the general partial-derivative expansion
d H = ( d H d T ) P d T + ( d H d P ) T d P ,
or replacing the partial derivatives with the corresponding material properties
d H = C P d T + V ( 1 α T ) d P ,
with constant-pressure heat capacity C P , temperature T, bulk modulus K, thermal expansion coefficient α, and volume V , for the specific cases of an ideal gas, for which α = 1 / T, or constant pressure ( d P = 0), thus giving d H = C P d T and then Δ H = C P d T
To calculate Δ S for instance, you'd express dS in the variables you wish to use, e.g.,
d S = ( d S d T ) P d T + ( d S d P ) T d P .
Then you'd figure out what material properties those partial derivatives refer to, simplify, and integrate over the temperature range of interest. Here, C P T ( S T ) P , so at constant pressure d S = C P T d T and then Δ S = C P T d T
The same general strategy would be applied to calculate Δ G
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