According to the ideal gas law, what happens to pressure if volume is doubled while keeping temperature constant?

To understand the relationship between pressure and volume in the context of the ideal gas law, we can refer to the equation itself: ( PV = nRT ), where ( P ) represents pressure, ( V ) represents volume, ( n ) is the number of moles, ( R ) is the universal gas constant, and ( T ) is the temperature in Kelvin.

When the volume of a gas is doubled while keeping the temperature constant (isothermal conditions), we analyze the equation under these conditions. Given that ( n ) and ( R ) are also constant, we can rearrange the equation to express pressure in terms of volume:

[ P = \frac{nRT}{V} ]

If the volume ( V ) is increased (doubled, in this case), the pressure ( P ) must adjust to maintain the equality. Specifically, if the volume increases to ( 2V ):

[ P_{\text{new}} = \frac{nRT}{2V} ]

This indicates that the new pressure is half of the original pressure:

[ P_{\text{new}} = \frac{P_{\text{original}}}{2} ]

Thus, when the