Question

What would happen to the density if the pressure increases by a factor of 2 and the temperature is halved?

Answer 1

For an ideal gas, P = d R T, where P is the pressure, d is density, R is the gas constant for an ideal gas, and T is the absolute temperature.

At constant T, P = d R => Pd (R=constant)

If temperature is constant, then pressure and density both increase in proportion to one another. Thus, if the pressure increases by a factor of 2 density also increases by 2

From ideal gas equation it is clear that density is inversely related to temperature

P = dRT => p/d =RT => 1/d T (at constant pressure)

Thus of the temperature is halved density will be doubled