Thermodynamics gas work done question

[Norton]

Homework Statement

In the temperature range 310K and 330K the pressure of a non ideal gas is related to volume V and temperature T by P=(24.9 J/K) T/V− (0.00662 J/K^2)T^2/V. How much work is done by the gas if it's temperature is raised from 310K to 320K whilst pressure held constant?

Homework Equations

P=(24.9 J/K) T/V− (0.00662 J/K^2)T^2/V

The Attempt at a Solution

I'm quite stumped on this one, initially I thought maybe something to do with W=NkT(ln)Vf/Vi, but I was wrong since the temperature has changed. I also tried using Q=n(Cp)(deltaT), but it is for an ideal gas and the question is talking about a non ideal gas. If someone could just give me a bit of a hand showing me the equations I should be using that would be great, since that is where I think I am falling down at the moment.

Thanks

 

[Andrew Mason]

Homework Statement

In the temperature range 310K and 330K the pressure of a non ideal gas is related to volume V and temperature T by P=(24.9 J/K) T/V− (0.00662 J/K^2)T^2/V. How much work is done by the gas if it's temperature is raised from 310K to 320K whilst pressure held constant?

The expression for V is in the form:

$$V = aT/P + bT^2/P$$

You want to find $\int PdV$. To do that, you need to find dV.

What is dV/dT if P is constant?

AM

 

[Norton]

Sorry I'm still lost. I understand the expression for V, but what happens when P is constant?

 

[Andrew Mason]

Sorry I'm still lost. I understand the expression for V, but what happens when P is constant?

It enables you to calculate work easily: $\int Pdv = P \int dV$.

AM