Vander Wall Gas Thermometer: Ideal Gas Law and Triple Point Calibration

[completenoob]

Homework Statement

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?

Homework Equations

Above

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)?

 

[Dadface]

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.

 

[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?

 

[Dadface]

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 into vans equation to find T.

 

[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.

 

[Dadface]

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.

 

[Dadface]

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

 

[Redbelly98]

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.

 

[Saqib]

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.

increase the size of molecule