# Vander Wall Eq.

1. Mar 1, 2009

### completenoob

1. The problem statement, all variables and given/known data
A constant volume gas thermometer of volume V contains n amount of moles of gas. Assume the gas obeys the ideal gas law pv=nRt. The behavior is better described by:
$$\left(p+a\frac{n^2}{V^2}\right)\left(\frac{V}{n}-b\right)=RT$$
a=0.1, b=3e^-5. The thermometer is calibrated at the triple point of water. How much will the temp measure in error at 100 C?

2. Relevant equations
Above

3. The attempt at a solution
I must be misinterpreting something. Do they mean error of the former with respect with the later?
Do I plug in temp for Vander, find pressure, plug that in for ideal gas law and find the temp?
The error being the difference between 100C-T(ideal)?

2. Mar 1, 2009

As far as I remember this the constant volume gas thermometer takes a series of readings and graphically extrapolates these to a zero pressure where the the gas is theoretically perfectly ideal.Therefore I think that with this example the ordinary ideal gas equation gives the most accurate answer.

3. Mar 2, 2009

### completenoob

But it even says explicitly that the behavior is better described by:Vander Wals.
My question still stands: Do they want me to find the error by finding the pressure in Vanders, plug that into the ideal gas equation and get a temperature? Then get the error?

4. Mar 2, 2009

Van der Waals is a much better approximation of how real gases behave but his equation approaches the ideal equation as P tends to zero.If the thermometer was used to take just one set of readings then van der waals would give the most accurate answer.If , however, the extrapolation technique I referred to was used then both equations would give the same and most accurate answer.Your question is a little unclear but I think they want you to assume that 100 degrees is the most accurate answer and they want you to plug values in to vans equation to find T.

5. Mar 2, 2009

### completenoob

Thanks for the response Dadface. But What would I plug into p? I would have two unknows: p and T.
Yah I know, the question they stated is kind of vague.

6. Mar 2, 2009

I think they want you to express the error in terms of P and V.Try multiplying out the brackets in vans equation and take it from there.

7. Mar 2, 2009

In fact multiplying out is probably not necessary.use vans equation, plug in the values you have and re arrange to get T

8. Mar 2, 2009

### Redbelly98

Staff Emeritus
You can figure out what V/n is (from van der Waal's equation) if you know P and T at the triple point.

Knowing V/n, you can figure out P (again from vdW eqn) when T=100C.

9. Apr 15, 2010

### Saqib

increase the size of molecule