- #1
danago
Gold Member
- 1,123
- 4
I am currently doing a class on chemical thermodynamics which involves a fair amount of calculus. So far it is going well, however i have a very quick question about the notation being used for partial derivatives.
If there is some property of a mixture, K=K(T,P), then the differential change in that propety is given by:
[tex]
dK = \left(\frac{\partial K}{\partial T}\right)_P dT + \left(\frac{\partial K}{\partial P}\right)_T dP
[/tex]
Where the subscripts T and P imply that they are being held constant. My question is -- Does the partial derivative not already imply everything except for one variable is held constant? Would [tex]\frac{\partial K}{\partial T}[/tex], by definition, be the change in K when ONLY T changes, without having to specift that P is held constant?
I guess what i am asking is -- is there is a difference between [tex]\frac{\partial K}{\partial T}[/tex] and [tex]\left(\frac{\partial K}{\partial T}\right)_P[/tex] that i was not made aware of in my first year calculus courses?
If there is some property of a mixture, K=K(T,P), then the differential change in that propety is given by:
[tex]
dK = \left(\frac{\partial K}{\partial T}\right)_P dT + \left(\frac{\partial K}{\partial P}\right)_T dP
[/tex]
Where the subscripts T and P imply that they are being held constant. My question is -- Does the partial derivative not already imply everything except for one variable is held constant? Would [tex]\frac{\partial K}{\partial T}[/tex], by definition, be the change in K when ONLY T changes, without having to specift that P is held constant?
I guess what i am asking is -- is there is a difference between [tex]\frac{\partial K}{\partial T}[/tex] and [tex]\left(\frac{\partial K}{\partial T}\right)_P[/tex] that i was not made aware of in my first year calculus courses?