If both the volume and absolute temperature of a confined gas are doubled, what happens to the pressure?

In this scenario, we can use the ideal gas law, which is expressed as ( PV = nRT ). In this equation, ( P ) stands for pressure, ( V ) is volume, ( n ) is the number of moles of gas, ( R ) is the universal gas constant, and ( T ) is the absolute temperature in Kelvin.

When both the volume and the absolute temperature of a confined gas are doubled, we can analyze how this affects the pressure. Let's denote the initial state of the gas as having an initial volume ( V ) and an initial temperature ( T ). The initial pressure can be represented as ( P ).

When the volume is doubled, it becomes ( 2V ), and when the temperature is doubled, it becomes ( 2T ). Substituting these new values into the ideal gas law gives us:

[ P' \times 2V = nR \times 2T ]

To isolate the new pressure ( P' ), we rearrange this equation:

[ P' = \frac{nR \times 2T}{2V} ]

Notice that the ( 2 ) in the numerator (from the doubling of