The volume of a monatomic ideal gas doubles in an isothermal expansion. by what factor does its pressure change?

The pressure of the gas changes by a factor of 2

Explanation:

An isothermal expansion is a process in which a gas expands (or contracts), keeping a constant temperature.

On the other hand, the expression for an Ideal Gas is:  

(1)

Where:  

is the pressure of the gas  

is the volume of the gas  

the number of moles of gas  

is the gas constant  

is the absolute temperature of the gas

Now, if the temperature keeps constant, we can use Boyle's law, which relates the volume and pressure of a certain amount of gas maintained at a constant temperature:

(2)

Where are the initial pressure and initial volume of the gas and are the final pressure and final volume of the gas.

If:

(3)

(4) where

Then:

(5)

(6)

(7)

Finally:

(8) This means the pressure of the gas changes by a factor of 2.