Ideal gas and mercury expansion in a glass thermometer

[evgreece]

Hi everyone,
I'm new to this forum so please don't throw any stones if my question is too naive. I have this problem and it's urgent that I give an answer very quickly...

We have a glass thermometer filled n moles of ideal gas (instead of vacuum). The thermometer has also mercury in it. We apply heat and the mercury expands. Because the thermometer is also filled with ideal gas (i.e. air) there will be a limit, where mercury will stop expanding, and the air won't compress anymore.
-For n moles of air and m moles of mercury, what are the equations describing this? (Assume that the glass won't break)
-What is going to happen when we continue to apply heat in terms of Pressure? (I know that pressure is going to increase, I just want the maths of it)
-How much can the ideal gas be compressed?

Thanks in advance

 

[mgb_phys]

The equation describing an ideal gas is PV = nRT
P = pressure, V = volume , T = temperature ( n is the amount (moles) of gas and R is a constant)
so this tells you that Pressure or volume go up as you apply heat.

An ideal gas can be compressed to nothing.

 

[evgreece]

Yeah, thanks, but my question is a little more complicated than this.
There are differential equations describing the constant 1/K (or B in some books) of the system. I know the pressure is going to keep going up, but there is a certain limit. An ideal gas can indeed compress to nothing, but if you see this in a real problem (i.e. a pump) you'll see that this isn't even close to nothing.
It's the differential equations I'm interested in, and the pressure between the m moles of mercury and the n moles of air.
Anyway, thanks again.

 

[mgb_phys]

The ideal gas is only slightly modified for real gases.
You added a volume term to account for the finite volume of the gas and a small attractive force for the Van der Waals forces.

( P + a / Vm2 )( Vm - b ) = R T

P = pressure
Vm = molar volume
R = ideal gas constant
T = temperature

where a and b are either determined empirically for each individual compound or estimated from the relations.
a = 27 R2 Tc2
--------
64 Pc

b = R Tc
----
8 Pc

Tc = critical temperature
Pc = critical pressure