# Temperature and pressure in a laboratory

• RafaelF13
In summary, the conversation is about a homework problem involving temperature, pressure, and the number of moles of air in a container. The equation PV=nRT is suggested as a possible solution, but there is uncertainty about how to set it up. The question also raises the issue of stability in a gravitational field. Ultimately, it is suggested that the problem may have an ambiguous or potentially open-ended solution.

## Homework Statement

The are temperature and pressure in a laboratory are 20 degree C and 1 atm. A 1L container is open to the air. The container is then sealed and placed in a bath of boiling water. After reaching thermal equilibrium, the container is opened. How many moles of air escaped?

## The Attempt at a Solution

No attempt. PV=RT but I am not sure how to set up the equation.

Welcome to PF;
You need to check that equation ... is this question part of a course?
Does the course have course-notes or lessons of some kind that you could peruse to get started?

Just from what you've written - would you say that the air in the container is hotter or colder than the surrounding air? Therefore, what do you normally expect for that situation if the container is opened?

Use PV=nRT, not PV = RT. How many moles of air were in the 1 liter container at 20 c and 1 atm? How many moles of air are in the 1 liter container if the air temperature is 100 c and the pressure is 1 atm?

@Chestermillar: that's probably what is intended all right - however, what is stopping all the hot air in the container leaving and cold air flowing in? Try it and see what happens? Maybe the container is opened at the bottom?

Simon Bridge said:
@Chestermillar: that's probably what is intended all right - however, what is stopping all the hot air in the container leaving and cold air flowing in? Try it and see what happens? Maybe the container is opened at the bottom?
Yes. I guess that's right. But the rapid outrush would happen first, and then the natural convection would happen slowly. However, strictly speaking, the equilibrium would be unstable in a gravitational field.

What if only a teenie tiny hole were used to open the container?

@Chestermillar: strictly speaking, the equilibrium (internal-external pressure) would be unstable anyway - but, in a gravitational field you get the hot-air wanting to float. And, with that, we've basically done the question for OP :)

@Steamking - you could make the example work if you had a bleed valve in the container and just bled off the hot air until the pressure equalized.

This is how teachers can shoot themselves in the foot by being too glib with the questions - but being too specific makes the answer too implicit in the question and it's not much of a test.

@RafaelF13: any of this help?
It is faintly possible that the person setting your homework wants you to notice the ambiguity and exploit it for bonus marks - I know I've been known to do that. However, if you go that route, I'd recommend also doing the implied question comparing the number of moles in a given volume at different temperatures.

Simon Bridge said:
@Chestermillar: strictly speaking, the equilibrium (internal-external pressure) would be unstable anyway - but, in a gravitational field you get the hot-air wanting to float. And, with that, we've basically done the question for OP :)

I guess I should have, more properly, used the words meta-stable equilibrium rather than unstable equilibrium in referring to a stratified situation in which the lower density liquid is on the bottom. The meta-stable equilibrium is both in hydrostatic equilibrium and thermodynamic equilibrium. However, the slightest disturbance will drive it to a more stable equilibrium.

Chet