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Give an expression for the temperature of an ideal gas in terms of pressure p, particle density per unit volume rho, and fundamental constants.

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The expression for the temperature is T = P/(ρ*R)

How to find the expression for the temperature?

The general expression for an ideal gas is:

PV = nRT

Where:

  • P is the pressure
  • V is the volume
  • n is the number of moles
  • R is the constant of the ideal gas
  • T is the temperature.

If we divide both sides by the volume we get:

P = (n/V)*R*T

And n/V is the particle density, then we get:

P = ρRT

Now we isolate T, the temperature, to get:

T = P/(ρ*R)

If you want to learn more about ideal gases, you can read:

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