Two connected vessels at different temperatures. Are their pressures equal?

Question

You have two vessels connected via tiny pipes to each other and to a pressurized container of "Ideal Gas". The two vessels are "insulated" and their temperature can be changed and maintained at any constant value. When you fill them with the gas, both vessels are at the same temperature. When filled to a desired pressure, you close off the supply container and a while later, close off both vessels (equal pressure in both vessels). Next, you change the temperature of one of them (for the sake of argument: you heat it) while maintaining the other at the original temperature. When you open valves to connect the two vessels to each other and let the pressures reach steady state value(s) what is the relation between pressure in the "colder" vessel to the pressure in the "warmer" vessel?
I do know the answer, and have even verified the theoretical predictions by experiments, I just want to see if you can determine the answer.

Sorry guys but none of your answers was correct. This problem describes a typical situation in industry where the process vessels are at much higher temperatures than pressure sensors can take. Consequently the pressure is measured at the end of a sample tube.
Obviously there is a steady state situation even when the temperatures are different (there go a few answers),
It does not matter whether the sampling tube is attached at the top, bottom, right or left side, or front or back (another question down)
Furthermore, the number density will not be equal in the two vessels.
The ratio of pressures is the same whether the ratio of volumes is 1 to 1 or 1 to 1000 it is related only to the absolute temperatures in the two vessels.

It was the ratio of pressures that i was looking for, and sorry guys and gals but you all failed.

Answer 1

Your first two answers are clearly wrong.

The ideal gas laws apply to closed systems, which this is not, but they can still be used with some care.

Now if one vessel is hotter than the other then there will clearly be a heat flow from one to the other. To enable some form of equilibrium, lets assume that each vessel is in a large heat reservoir that keeps its temperature stable (that is, they are NOT insulated but are ISOTHERMAL). Lets also assume they have the same volume - and so contain the same mass of gas initially.

Because the vessels are connected their pressures *must* be the same.

So what happens when you open the valve? Well, the gas law tells you that at the same pressure gas in the the hotter container will try to occupy more volume. It cannot, and so there must be a flow of gas to the cooler container. Equilibrium will be reached when the mass of gas in the hotter container is sufficiently reduced that the gas laws can give the same pressure in each container for the given temperature difference. The form of the laws you need to deduce this is PV = nRT.

Answer 2

Ok, this is a bit of a loaded trick question, but here goes, but you didn't really specify if the tiny pipe is at the top or bottom of the container, I will assume top.There will really be no steady state value until both containers reach the same tempeature. The molecules in the warmer container are more excited with energy and will be creating more pressure , but it will be constantly cascading to the colder lower pressure container. Go ahead, blow me out of the water! Speel checker is out of ordr,sorry!

Answer 3

PV/KT=constant.

so if the pressure reaches steady values, then the temperature in both container are equal or the volume /temperature remains the same,

Since presure is proportional to temperature/Volume

Answer 4

The pressure in the warmer tank will be higher (due to Boyle's Law) so there will be gas flow into the cooler tank.