According to the ideal gas law, which describes the behavior of an ideal gas, the pressure (P), volume (V), and temperature (T) of a gas are related. The ideal gas law is expressed as:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
If the temperature and volume of a gas are both doubled while keeping the number of moles and the gas constant constant, the pressure will also double. This relationship can be observed by rearranging the ideal gas law equation:
P1V1 / T1 = P2V2 / T2
where P1, V1, and T1 represent the initial pressure, volume, and temperature, respectively, and P2, V2, and T2 represent the final pressure, volume, and temperature, respectively.
If we double the temperature (T2 = 2T1) and double the volume (V2 = 2V1), the equation becomes:
P1V1 / T1 = (2P1)(2V1) / (2T1)
Simplifying the equation gives:
P1V1 / T1 = 4P1V1 / 2T1
By canceling out the common terms, we get:
1 / T1 = 4 / 2
T1 = 2
Thus, the pressure ratio becomes:
P2 = 2P1
This means that the pressure will double when both temperature and volume are doubled, assuming the number of moles and the gas constant remain constant.