Why does pressure increase with increasing volume?

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Answer 1 · 2017-12-26T02:32:31

Um, no. Pressure decreases with increasing volume.

A positive slope of a pressure #P# vs. temperature #T# graph suggests that #P# increases with increasing #T#.
A positive slope of a volume #V# vs. temperature #T# graph suggests that #V# increases with increasing #T#.

If #Puarr# corresponds to #Tuarr#, it suggests that #P prop T#. If #Vuarr# corresponds to #Tuarr#, it suggests that #V prop T#.

But it does not work the way you think it does: the relationships do NOT form a syllogism.

Instead, two things proportional to the same quantity are inversely proportional to each other...

For ideal gases, this just puts the ideal gas law up against experiment:

#PV = nRT#

In a closed container, the total mols of gas are constant, so really, #(PV)/T = "const"#. And here we can clearly see that #P prop 1/V#:

#P = (nRT)/V#,

i.e. #P = "const" cdot T/V#, or #P prop 1/V#.