Displacement and electric field

[chemphys1]

Homework Statement

displacement and electric field related by D=εE where dielectric constant depends on volume and temperature. Express dD in terms of dV, dT and dE

(this is just a part of a question but want to make sure I have it right else the rest of the 'showing' and proofs are never going to work out)

The Attempt at a Solution

so taking D=εE

Then dD = εdV (because it is volume dependent) + εdT (temperature dependent)

what happens to the E, is it Edε + edE as well as the above
although it can't be dε because it says express in terms of dT dV and dE, no dε mentioned?

is any of that on the right lines?

any help appreciated

 

[haruspex]

D=εE where dielectric constant depends on volume and temperature.

We can write that predicate statement as ε = ε(V, T).
Based on that, you need to find an expression for dε in terms of dV and dT.
What would be the change in ε if T stays constant and V increases by dV?

 

[rude man]

... dielectric constant depends on volume and temperature. although it can't be dε because it says express in terms of dT dV and dE, no dε mentioned?

/QUOTE]

The above is self-contradicory.

How can there be no dε when it says ε varies with T and V?

 

[chemphys1]

We can write that predicate statement as ε = ε(V, T).
Based on that, you need to find an expression for dε in terms of dV and dT.
What would be the change in ε if T stays constant and V increases by dV?

as in like this?

dε = (∂ε/∂V)dV + (∂ε/∂T)dT

where does dD =
come into this?

 

[chemphys1]

... dielectric constant depends on volume and temperature. although it can't be dε because it says express in terms of dT dV and dE, no dε mentioned?

/QUOTE]

The above is self-contradicory.

How can there be no dε when it says ε varies with T and V?

true
I'm not very good at interpreting what maths questions mean/are saying

 

[chemphys1]

come up with this

dD = E∂ε + εdE

where

dε = (∂ε/∂V)dV + (∂ε/∂T)dT

overall

dD = E [(∂ε/∂V)dV + (∂ε/∂T)dT] + εdE

is that what I should be getting?

 

[rude man]

come up with this

dD = Edε + εdE

where

dε = (∂ε/∂V)dV + (∂ε/∂T)dT

overall

dD = E [(∂ε/∂V)dV + (∂ε/∂T)dT] + εdE

is that what I should be getting?

Excellent!