How fast does density change in an isobaric system?

[simple_logic]

Suppose the following

• an isobaric system
• an ideal heater⁽¹⁾ of infinite area on a single plane in a STP environment
• the heater is set to a given temperature

At a given distance perpendicular to the heater surface, what will the density of the gas be over time?

I spent a good part of the day getting nowhere, hopefully someone here can help.

Thank you,

S.L.

¹: All gas particle interactions with the heater result in the gas particle leaving at the set temperature of the heater

 

[Simon Bridge]

If you are asked for the density p(x,t) then there isn't enough information - without equilibrium there may be eddies and currents in the gas giving chaotic density fluctuations at any point. Presumably there is something else to take into account?

 

[simple_logic]

I would speculate that in an idealized system, this would be a function of the mean air particle speed, the mean collision frequency, energy accommodation coefficient, and possibly some relaxation constant/coefficient.

We can simplify the problem further by changing the STP environment to an infinite volume of 100kPa Argon at 293.2K

I'm interested in the approximate time it takes to get to equilibrium, and the quadratic relationship to distance.

Any takers?

 

[Aero51]

Look for a Navier-Stokes solver, it will get you an answer within 15% accuracy.

 

[PJC01]

In an isobaric system, where pressure is kept constant, the density of the gas will change over time due to changes in temperature. In this specific scenario, where an ideal heater of infinite area is used to heat the gas to a certain temperature, the density will change as the temperature increases. This is because as the gas particles interact with the heater and are heated to a higher temperature, they will have more kinetic energy and thus move faster. This increase in speed will result in the gas particles occupying a larger volume, leading to a decrease in density.

The rate at which the density changes will depend on the rate at which the gas is heated and the specific properties of the gas, such as its heat capacity and thermal conductivity. However, in an ideal system where all gas particle interactions with the heater result in the gas particles leaving at the set temperature, the density change should occur relatively quickly.

To determine the exact rate of density change over time, one would need to consider the specific conditions of the system and perform calculations using thermodynamic principles. Additionally, the distance from the heater surface would also play a role in the density change, as the gas particles further away from the heater may not be as affected by the heating and thus may have a slower rate of density change.

In summary, the density of a gas in an isobaric system will change over time as a result of heating from an ideal heater. The exact rate of change will depend on various factors and can be determined through calculations.