Equations of state -- Partial derivatives & Expansivity

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1. Mar 12, 2015

Mia_S

1. The problem statement, all variables and given/known data

Show that the coefficient of volume expansion can be expressed as

β= -1÷ρ (∂ρ÷∂T) keeping P (pressure) constant
Where rho is the density
T is Temperature
2. Relevant equations
1/v =ρ
β= 1/v (∂v÷∂T) keeping P (pressure ) constant

3. The attempt at a solution
I started with the original equation (β= 1/v (∂v÷∂T) ) ,substituted ρ for 1/v and got stuck . What should I do next? What's the solution?

Thank you!

2. Mar 12, 2015

Bystander

"Stuck" where?

3. Mar 12, 2015

Mia_S

Here, β= ρ(∂v÷∂T)

4. Mar 12, 2015

Bystander

You're using "ρ = 1/v," so what's the next step?

5. Mar 12, 2015

Mia_S

I don't know :( ...Should I change the partial derivative to 1/(∂T÷∂v) ?

6. Mar 12, 2015

nuclear_chris

May I suggest you use the chain rule of derivatives since V=1/rho=(rho)^-1. Take the derivative of the outside function times the derivative of the inside.

7. Mar 12, 2015

Staff: Mentor

If v = 1/ρ, then, in terms of ρ and dρ, dv = ??

Chet

8. Mar 17, 2015

Mia_S

I got it! Thank you :)