Confused about Boyle's Law, Charles' Law and the pressure Law?

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Boyle's Law states that pressure multiplied by volume equals a constant (pV=C), while Charles' Law indicates that volume divided by temperature equals a constant (V/T=C). The confusion arises when attempting to derive the pressure law (P/T=C) from these two equations. Dividing Boyle's Law by Charles' Law leads to pT=C, which differs from the textbook's pressure law equation. The distinction lies in the conditions of the laws: Boyle's Law assumes constant temperature, whereas Charles' Law assumes constant pressure, complicating their combination. Understanding the conditions of each law is crucial for correctly applying them in thermodynamic equations.
21joanna12
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In my textbook, it says that pV=C (Boyle's Law), V/T=C (Charle's Law) and that P/T=C (pressure Law). The problem is that I cannot see how the first two equations combine to give the last one. If I divide the first equation by the second, I get that pT=C, which certainly is not the same as the equation given in my textbook. I'm not sure if maybe you cannot combine these two equations because Boyl's law assumes constant temperature but Charle's Law assumes constant pressure? Although I don't see why that would mean you cannot combine them...

I'm not sure if I should have posted this here or in classical physics, so I will move it if necessary.

Thank you in advance!
 
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I've done this using boyles law and the pressure law, but you can do the same thing using Boyles law and Charles law
 
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