Pressure distribution of ideal gas under non-uniform temperature

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SUMMARY

The discussion centers on the pressure distribution of an ideal gas in a square box subjected to a temperature gradient, where one side is heated while the opposite side remains at room temperature. It is established that, under these conditions, the ideal gas law applies locally, leading to non-uniform density due to the temperature difference, while pressure remains uniform throughout the container. The temperature gradient creates a situation where density varies to maintain the ideal gas law, confirming that in this scenario, density is the variable that changes, not pressure.

PREREQUISITES
  • Understanding of the Ideal Gas Law
  • Basic principles of thermodynamics
  • Knowledge of heat transfer concepts
  • Familiarity with pressure and density relationships in gases
NEXT STEPS
  • Study the Ideal Gas Law and its applications in varying temperature conditions
  • Research heat transfer mechanisms, particularly conduction and convection
  • Explore the concept of density variations in gases under thermal gradients
  • Learn about the implications of non-uniform pressure and density in fluid dynamics
USEFUL FOR

This discussion is beneficial for physicists, engineers, and students studying thermodynamics, particularly those interested in gas behavior under varying thermal conditions.

Margalit
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Suppose there is a square box with an ideal gas inside at standard temperature and pressure. Now one side of the box is heated up while the other opposite side remains at room temperature (assume a large heat sink). It is clear the temperature distribution of the gas inside the chamber will have a gradient. Assume that the temperature difference is not larger (a few degrees Kelvin), so that convection is not a major driver. If the ideal gas law is followed locally in the space between the walls, the difference in temperature means that either one or both of the pressure or gas density must non-uniform to compensate the variable temperature.

My question is as follows: In this situation is the pressure or density or both non-uniform between the walls?
 
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Generally, in a container, the pressure will be uniform throughout. In this case, the density is what will be non-uniform.
 

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