The absolute temperature of the ideal gas was doubled. How should its mass be changed so that

The absolute temperature of the ideal gas was doubled. How should its mass be changed so that, with a constant volume, its pressure would increase by 4 times?

The state of an ideal gas is described by the Clapeyron-Mendeleev formula:

PV = mRT / M, where P, V, T – pressure, volume and absolute temperature, respectively, m – gas mass, R – universal gas constant, M – molar mass.

We find the dependence of pressure on mass, volume and temperature:

P = (mRT) / (MV) (1).

After changing the mass to the value m1 and the temperature to the value 2T, the pressure increased 4 times:

4P = (m1R * 2T) / (MV) (2).

From (1) and (2) we find the initial and modified masses:

m = (MPV) / RT;

m1 = (M * 4P * V) / (R * 2T) = (2MPV) / (RT).

Mass ratio:

m1 / m = ((2MPV) / (RT)) / ((MPV) / (RT)) = 2.

m1 = 2m.

The correct answer is to double it.