Understanding Gas Laws: Boyle's, Charles', and the Conceptual 'What If' Question

[pibomb]

This is an absurd question, but the answer is beyond me:

According to Boyle's Law, we get the relationship: P=k/V (k=constant)
According to Charles' Law, we get: V/T=k
And, P/T=k

My question is rather an conceptual "what if": if we increase, say, the volume of the an ideal gas, it's pressure would go down. Yet, an increase in volume should lead to an increase in temperature, and this an increase in pressure. This can't be right, and though I know I'm missing something fundamental, I can't figure out what that is.

 

[montoyas7940]

The problem is you are considering two different conditions; one at V1 and another at V2.

Charles law for two conditions is V1/T1=V2/T2 and P1/T1=P2/T2.

Hope this helps.

 

[pibomb]

Oh I see, thanks.

 

[Mapes]

This is not an absurd question at all. But here is the problem: Boyle's and Charles' Laws are simplifications of a more complex relationship for ideal gases. To stay simple, each Law needs to assume that all other variables are constant. For example, P=k/V assumes constant temperature, V/T=k assumes constant pressure, and P/T=k assumes constant volume. This is why your thought experiment didn't work.

So if you want to work with changes in multiple variables (which is usually the case in real systems), you need the more general equations

$$pV=nRT\quad\quad U=cRT$$

the first of which is the ideal gas law and the second is the relationship between energy and temperature for an ideal gas.