# Keeping #n# and #T# constant, how do I prove that #P prop 1/V#? What about keeping #n# and #P# constant and showing that #V prop T#?

##### 1 Answer

You can check this just from the ideal gas law.

#PV = nRT#

If you try to double the pressure, then you are clearly increasing it. As a result, what do you have to do to get

#2PV = nRT#

#=> 2P*1/2V = nRT#

Therefore, the volume must have halved to cancel out the pressure doubling. In general, it means

You can also prove it further:

#P = nRT*1/V#

Therefore,

Can you show that

#V = (nR)/P*T#