Fluids: Liquids and Gases

Equation

PV = nRT    or

P = nRT/V   or

P = (nR/V) * T

4.6

Equation

P  T

4.7

Equation

P 1 / V    or
V
1 / P

4.8

Pressure in Gases

Ideal Gas Law

Put Boyles Law and Charles and Gay-Lussac's Law together and we get the "Ideal Gas Law."

In a given volume of gas (i.e., both the volume and the number of moles of gases are constant), the pressure is directly proportional to Kelvin temperature. In other words, increasing temperature increases the pressure. Visualize gas molecules having higher energy and moving faster at higher temperatures, with more frequent and energetic collisions.

Pressure x volume = number of moles x universal gas constant x temperature, all divided by volumePV = nRT    or P = nRT/V   or P = (nR/V) * T

Where:

P = Pressure

n = number of moles of a substances (n x 6.022 x 1023 molecules – that’s a BIG number!)

R = the universal gas constant = 8.31 J/mol-K (mol = a mole)

V = volume

T = temperature, Kelvin or K (Kelvin = 273 + degrees Celsius)

PV=nRT is called the Ideal Gas Law.

Since R is already a constant, and we aren’t changing n or V, we can substitute C (representing a constant) for nR/V.

Thus, P = CT  or:

Pressure is directly proportional to temperature P  T

This is how a pressure cooker operates. As the temperature goes up, so does the pressure. And at higher pressure the water in the cooker can become hotter than the boiling temperature at normal pressure. Hot steam penetrates the food so that it cooks faster.

Inversely, if we hold the temperature constant, but vary the pressure – e.g., by squeezing on a small, sealed balloon, thus decreasing the volume – the pressure goes up until the balloon will eventually burst. In this case the number of molecules and temperature are held constant, so

P = nRT / V and with n and T constant, then C = nRT

P = C / V is proportional to:

Pressure is inversely proportional to volume 1 / V    or    V  1 / P

When pressure increases, the volume does the opposite – it decreases. Likewise, if we release the squeezed balloon mentioned above, the volume increases and the pressure inside decreases. This is just another way of stating Boyle’s Law, PV = constant.

These gas relationships are easy to remember. When pressure increases the gas molecules are pushed closer together so that their volume decreases, and the temperature increases because energy was added by increasing pressure.

If variable is increased

VTn
Then Pressure

decreasesincreasesincreases

The universal gas constant, R, in the ideal gas law equation, was first introduced in 1874 by Russian scientist Dmitri Mendeleev to replace a large number of specific gas constants. For that and other contributions – especially inventing the Periodic Table - a crater on the Moon was named to honor him.

Most gases act like ideal gases at non-extreme temperatures and pressures. At extremes, forces between molecules are important, and more complex laws govern their actions.