# Pressure of a gas

In a recent physics class, I was told that for a gas enclosed in a closed vessel the pressure of the gas is variable but the volume and amount remains constant if we heat the gas. I understood this - simply as molecules can't escape out of closed vessel and still have same free space for moving.

Then I was told that if we consider gas in an open vessel and heat it, then its volume and pressure will be constant, then its molecules may escape, therefore the amount of gas cannot be constant on changing other conditions. Now I have the following doubts about this statement:

1. Why will pressure remain constant if we heat the open container, as molecules will start moving more swiftly therefore will exert more pressure on walls.
2. Why will volume be constant for the gas in open vessel, as volume is the free space available to gas for motion and in an open vessel whole universe is available to gas for motion.

• for a gas enclosed in a closed vessel the pressure of the gas is variable This is simply wrong. the pressure of a gas in closed vessel is constant everywhere throughout the volume, unless there are other forces/interactions acting on some gas molecules throughout different regions in the volume. if we consider gas in an open vessel, then its volume and pressure will be constant How is that even possible? You are increasing the available volume for the gas. Where are you getting this information? Is there something else happening here that you have not stated? Commented May 23, 2021 at 3:52
• Are you talking about a particular mass of the gas? the volume of the vessel? Commented May 23, 2021 at 3:57
• Most likely he refers to pressure changes over time as temperature changes in a sealed container, rather than anisotropic pressures within the volume at a single moment. Commented May 23, 2021 at 5:23
• @joseph , sorry I made things a little complicated, what I want to simply ask is that if we have an open container and e heat why will the pressure of gas in the container will equalize with atmospheric pressure since gas inside would have molecules moving more swiftly therefore imparting large pressure to the container Commented May 23, 2021 at 7:30
• I see. The thing is, even though the vessel is being heated, as much gas that is leaving it will enter it. Though it may be the case that right at the point where the heat is applied, perhaps the pressure there maybe slightly higher. But on the whole, the vessel and the surroundings are pretty much in pressure equilibrium. Cheers. Commented May 23, 2021 at 7:42

The air pressure inside a closed container may increase or decrease with temperature changes over time. The volume will remain the same as long as the container is rigid and does not change size. The amount of gas does not change in the closed container as the amount of gas molecules, its mass, does not change. As you say you understand this part I will move onto your questions, number 1. When you heat an open container the pressure remains the same because the excited molecules may bounce off of the walls of the container as you assumed, however they do not bounce off of the open top, so gas molecules can escape into the atmosphere allowing for no pressure increase. Question number 2. The volume of gas IN the open container remains the same. Gas molecules may enter or exit the open container, but the volume of gas inside the container at different moments will remain the same. For example a 1 liter open container will always have 1 liter of volume considered to be inside of it.

• so you give me a crisp and clear explanation question 2 but I couldn't gather much from answer of question 1, please help Commented May 23, 2021 at 7:13
• see my comment above so you can get to know what my doubt is Commented May 23, 2021 at 7:34
• The open container has no top or lid to contain gas molecules so they are free to enter or exit the inside of the container. therefore as the gas inside heats up and the molecules move faster more of them will exit through the open top so less molecules moving faster in the warmer container equals the pressure of more molecules that are moving slower in the cooler container. Two unconstrained areas of gas in open contact will reach equal pressures. Commented May 23, 2021 at 7:52
• now I understood that "two unconstrained area of gas will reach equalize pressure" and the correct reason behind it. Commented May 23, 2021 at 7:56
• but now what i doubt is why they will equalize to atmospheric pressure Commented May 23, 2021 at 7:56

I think the statements are dependent on the interpretation of the state function of the ideal gas

$$PV=nRT$$ or $$=NkT$$

n the number of moles, N the number of molecules

For the closed case, the pressure will vary if the temperature varies, whereas the volume and number of molecules is fixed .

For the open case the interpretation is wrong, it is ignoring the number of molecules. When the vessel is open, the pressure will equalize with the atmospheric but a number of molecules will escape or increase depending whether it was higher or lower than atmospheric pressure before opening.

Why will pressure remain constant if we heat the open container, as molecules will start moving more swiftly therefore will exert more pressure on walls.

If we take an open pot, its volume is constant, even if you heat the air, the volume cannot change, nor the atmospheric pressure. The number of molecules will change though

Why will volume be constant for the gas in open vessel, as volume is the free space available to gas for motion and in an open vessel whole universe is available to gas for motion.

The volume is constant for a vessel, it is the number of molecules that will decrease or increase if the temperature is made higher or lower.

• $pressure$ $will$ $equalize$ $with$ $atmospheric$, what's the reason behind this, that only I want to know. Commented May 23, 2021 at 7:27
• look at this link hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/idegas.html .It is a result of the ideal gas law. Commented May 23, 2021 at 8:11
• In a sense the equalization happens because the vessel cannot be considered a separate volume from the larger atmosphere volume once open, as you also observe. Commented May 23, 2021 at 8:23