A simple approach is with the ideal gas law.

PV = nRT

P is pressure, n absolute terms (that, a perfect vacuum is 0 psi)

V is volume

n is number of

moles of gas (a mole is a fixed number of atoms or molecules of a substance,

moles therefore represent mass)

R is the ideal gas constant

T is temperature, absolute

Because the volume of the container is constant, V is a constant. For all

practical purposes, the temperature of the low pressure tank is the same as the high pressure tank and can be considered a constant.

In the problem, (Is a pressurized tank heavier than a low pressure tank?), pressure goes up compared to the low pressure tank.

Now re-arrange the equation ideal gas law equation so the constants are on one side:

V/RT = n/P

Label pressurized case “1” and low pressure case “2”,

V/RT = n1/P1 = n2/P2

n1/P1 = n2/P2

P1 is greater than P2, so to balance the equation, n1 must be greater than n2.

(Or re-arrange again:

P1/P2 = n1/n2

P1/P2 is greater than 1, therefore, n1/n2 is greater than 1.)

More mass is added in the pressurized case, so the pressurized case is heavier. (How much heavier is a function of the tank volume.)

The weight proportion of gas in a 150 psig (psi

gauge) to the empty tank (0 psig)? Convert the pressure to absolute by adding atmospheric pressure, about 14.7 psia. (“a” for absolute) (A “

gauge” pressure is usually relative to atmospheric pressure. 0 psig then on a tank means nothing will leak out or in.) I’m going to cheat a little and round 14.7 psia up to 15 psia, so the ratio is:

(150 + 15)/(0+15) = 165/15 = 11

So there is 11 times the mass of gas in the pressurized tank than in the empty tank.

Now say the tank volume is 1 cubic

foot, and typical air density at atmospheric conditions and typical temperature is about 0.075 pound per cubic feet,

The weight of air in the low pressure (0 psig) tank is 0.075 pounds, and the weight of air in the pressurized tank weighs about 0.075 x 11 = 0.825 pounds.

[That's not quite ship's example, but it can be seen that it's not much added weight. ship's tank at the example pressure would be about twice the weight - 1.6 pounds.]

Joe