# Isothermal increase in pressure of solids

1. Jun 29, 2007

### ch1000_man

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

How do you express work in an isothermal increase of pressure of a solid in terms of the initial and final pressure?

2. Relevant equations

van der waals equation

W=Integral of PdV

(P-na/v^2)(v-nb)=nKT

P=pressure
V=volume
n=number of molecules(constant)
T=temperature(constant)

3. The attempt at a solution

d/dV[(P-na/V^2)(V-nb)=nKT]*

The problem here is that dP and dV are very hard to separate so it is hard to substitute dP in W=integral of PdV.

2. Jun 29, 2007

### siddharth

(i) Why are you using the Van der waal equation of state for a solid, as it's usually valid only for real gases?

(ii) From my thermodynamics course, one of the empirical equation of states I used for a solid was

$$V(p,T) = a +bT +cT^2 - d (p) + e (p T)$$

where a,b,c,d,e are empirical constants depending on the substance.

This is valid for a fairly wide range of T and P. You should be able to find this in a handbook or a table. (or, http://www.ccl.net/cca/documents/dyoung/topics-orig/eq_state.html" [Broken])

Last edited by a moderator: May 2, 2017
3. Jun 30, 2007

### ch1000_man

I was really doubtful using the van der waals equation because most of the problems I encountered used this equation and it just so happened that all of them involved gases though I wasn't sure if van der waals was just limited to real gases. I thought it was a general equation. :)

I tried looking for an equation for solids but I just keep finding the van der waals eqn and the ideal gas eqn.

Anyway thanks, I'll try to use this and find an expression of work and I'll post it here.