According to the ideal gas law, what happens to the volume of a gas when the temperature doubles(all else held constant)

The volume will double too

Explanation:

The ideal gas law is the following:

PV = nRT

Now, in order to know what happens to the volume of a gas if temperature is doubled, let's write an expression for temperature for both conditions:

T1 = PV1/nR

T2 = PV2/nR

We know that Temperature is being duplicated so T2 = 2T1. Replacing in the expression we have:

2T1 = PV2/nR

Replacing T1 here we have:

2PV1/nR = PV2/nR

In this expression, P, n and R cancels out, because they remain constant so, all we have left is:

2V1 = V2

This means that if we double the temperature, the volume will double too and they directly proportional to pressure and temperature.