# Partial Temperature of a Gas in a Mixture

• hairless_ape
In summary, the conversation discusses the concept of partial temperature in a gas mixture and its potential application in the Maxwell's demon paradox. The participants mention the principles of elastic collisions and dynamic equilibrium, and how they relate to the concept of partial temperature. They also discuss the role of partial temperature in determining the total temperature of a gas mixture, and how it differs from the concept of partial pressure. It is noted that partial temperature is not a commonly used concept, but it may have relevance in certain scenarios involving multiple gas components.
hairless_ape
Is there such a thing as a partial temperature of a gas in a mixture? Partial pressure is commonly accounted for and used. It seems that if there are molecules of different masses colliding in a mixture, their average respective velocities in a mixture should be different based on transfer of momentum and conservation of energy equations. Am I missing something?

Also if this is a thing, wouldn't there be an application regarding Maxwell's demon paradox? For example if a mesh small enough to only allow single atoms through is used to separate chambers in a gas mixture container?

If the gas is equilibrium, all components have the same temperature, otherwise heat would flow between them until they did.

If the gas is equilibrium, all components have the same temperature, otherwise heat would flow between them until they did.

Thanks for the reply. If by same temperature you mean the same molecule velocity, is where I am not quite clear. We typically assume elastic collisions between gas molecules. If two objects of different masses undergo an elastic collision starting at equal and opposite velocities, the magnitudes of resulting velocities would be different.
As for flow of heat/energy, I would argue that the dynamic equilibrium principle can apply here. More over temperature is a macroscopic quantity, it would be highly unlikely for all molecules in an even homogeneous substance to be moving at the same velocity at least based on what I've known, which isn't very much clearly...

Even a single component gas at temperature T does not have its molecules moving at the same velocity. It's a distribution.

jim mcnamara
Temperature is a measure the average kinetic energy of the molecules in a gas. In a gas at equilibrium with different components, all components have the same temperature and hence the same average energy, as @Vanadium 50 said. The heavier molecules will have a slower average velocity than the lighter molecules, because energy is 1/2 mv^2.

sophiecentaur
I think partial temperature can be relevant in a specific scenario.
We think about partial pressure when we take, say 3 boxes of different gas species, all in the same temperature and volume, and combine them into one box (which again has the same temperature and volume). Then, the total pressure of the combined box is dependent on the partial pressure, i.e., the pressure of each of the original boxes.

Say we do the following experiment: again we take 3 boxes, but this time each box has the same volume and same pressure, but not necessarily the same temperature. The temperature of each box is now dependent on the number of moles in the box and we call this the partial temperature.
When we combine the boxes into a new box, which still has the same pressure and volume, the new temperature will depend in some way on the partial temperatures of the 3 boxes.

However, the relationship is not as straightforward as in the partial pressure case because temperature, in the ideal gas case, is not linearly proportional to the number of moles, n, but on 1/n. I think in this case the total temperature will have an equation of the form 1/T = n1/T1 + n2/T2 + n3/T3, where T1, T2, T3 are the partial temperatures.

This is a strange experiment to do but it is the only case I can think of of where partial temperature might be relevant.

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## 1. What is the partial temperature of a gas in a mixture?

The partial temperature of a gas in a mixture refers to the temperature of a specific gas component within the mixture. It is the temperature that the gas would have if it occupied the entire volume of the mixture at the same pressure.

## 2. How is the partial temperature of a gas in a mixture calculated?

The partial temperature of a gas in a mixture can be calculated using the ideal gas law, which states that the product of pressure and volume is directly proportional to the number of moles of the gas and its temperature. By rearranging the equation, the partial temperature can be calculated by dividing the product of pressure and volume by the number of moles of the specific gas component.

## 3. Why is it important to know the partial temperature of a gas in a mixture?

Knowing the partial temperature of a gas in a mixture is important because it allows us to understand the behavior and properties of the individual gas component within the mixture. This information is crucial in various industrial and scientific applications, such as in the production and storage of gases, as well as in the study of chemical reactions.

## 4. Can the partial temperature of a gas in a mixture change?

Yes, the partial temperature of a gas in a mixture can change depending on the conditions of the mixture. If the pressure, volume, or number of moles of the gas component changes, the partial temperature will also change accordingly. Additionally, changes in the temperature of the entire mixture can also affect the partial temperature of the gas component.

## 5. How does the partial temperature of a gas in a mixture relate to the overall temperature of the mixture?

The partial temperature of a gas in a mixture is directly related to the overall temperature of the mixture. In an ideal gas mixture, the partial temperatures of all gas components will be equal to the overall temperature of the mixture. However, in non-ideal gas mixtures, the partial temperatures may vary and will depend on the interactions between the different gas components.

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