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So Charles law states that when volume is not constant and you heat up a gas, the pressure stays constant. Example, if I have a syringe and I heat up the gas in the syringe, the syringe in would increase in volume and pressure by the gas in the syringe would remain constant.

However, if I have a manometer, left side exposed to atmospheric pressure and right side connected to a gas flask. Then I heat the gas flask. We know that the liquid level drops in the right side and liquid level rises in the left side. ie, the volume of the gas in the gas flask also increases since liquid level dropped. BUT, we also know from basics of pressure that pressure in the gas flask increased.

So my question is, why doesn't Charles law apply to this scenario where pressure should remain constant? Isn't the gas flask the same thing as a gas syringe, just that now the piston of the syringe is replaced with liquid.

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    $\begingroup$ Charlles law tells you how the volume $V$ changes when $P$ is held constant. The pressure $P$ is only constant when $V$ is allowed to expand without any restriction. But in the manometer the weight of the mercury constrains the expansion, so Charles does not apply. $\endgroup$
    – mike stone
    Mar 28, 2021 at 15:11

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The height difference of the liquid in the manometer shows that there is a pressure difference

$P=h\rho g$.

where $\rho$ is the density of the liquid.

If one side was at constant atmospheric pressure, but the liquid level dropped, it's showing a change in pressure and Charles law couldn't apply.

Depending on the details of the syringe or 'piston': sometimes it's just the weight at the top of a piston that keeps a gas under constant pressure. This time the weight can rise or fall, but since it exerts the same force, its weight, on the gas and the area is the same, then the pressure in that situation is constant and Charles law can apply.

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  • $\begingroup$ Yea I understand that since P = rho × h × g, there is a change in pressure. But I dont understand how this is different from a syringe. A syringe also has atmospheric pressure acting on the pistion too, just like how atm pressure is acting on the liquid. $\endgroup$ Mar 29, 2021 at 12:01
  • $\begingroup$ In the manometer there is atmospheric pressure plus the weight of the column of mercury due to the height difference of the columns. In the piston there is just the constant atmospheric pressure $\endgroup$ Mar 29, 2021 at 12:07
  • $\begingroup$ Ahhhh I see it now, so the pressure is not constant because the external pressure is not constant to begin with. Okay Im so dumb. Thank you so much!! $\endgroup$ Mar 29, 2021 at 14:56

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