[Physics] What happens to temperature as volume increases (charles law)

ideal-gasstatistical mechanicstemperaturethermodynamicsvolume

Let us take Boyles law to start.

Assumptions:

  • Gas is perfect.
  • In a massless piston that can be expanded with no friction
  • Adiabatic

If we were to decrease the volume of the piston, the pressure inside would go up because the gas molecules would be hitting the sides more often.

If we were to increase the outside pressure on the piston, the volume of the piston would go down until the internal pressure matched the external pressure.

We see here that Boyle's law is perfectly explained by the kinetic model of gases (T held constant).

Let's look at Charles law (P held constant)

If we were to increase the temperature of the molecules, their kinetic energy would increase and would therefore hit the piston with greater force and increase the volume of the piston until the internal and external pressures are equal.

But if we were to spontaneously increase the volume of the piston, the temperature would NOT increase as a result (to maintain the increased volume against the constant external pressure) because heat doesn't spontaneously arise.

So it seems that Charles law only works one way, but not the other. And that T and V are not intrinsically linked like P and V are in Boyles law. Is this true?

Best Answer

The answer itself is hidden in the second part of your question. P in any gas law refers to the pressure inside the volume of the container [ which is always equal to the external pressure on the container ]

Now, in the second part of your question, the statements

(P held constant)

&

if we were to spontaneously increase the volume of the piston

cannot be true simultaneously.

As soon as you want to increase the volume of the container (irrespective of the method of achieving such a change -- whether by a reversible piston process or via irreversible free expansion), you have to reduce the external pressure on the piston & thereby the pressure inside the container also reduces & then you can apply kinetic theory accordingly [ Note that unless these two P's are equal, you cannot apply any gas law because they are valid only for equilibrium situations. It's very important to keep this condition in mind when you are thinking about such thought experiments. ]

To conclude, all gas laws work irrespective of whether the change in the variables are positive or negative as long as you are being careful to satisfy all conditions including the condition of equilibrium & reversibility.

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