Cracking the SAT Physics Subject Test

THE IDEAL GAS LAW

Three physical properties—pressure (P ), volume (V ), and temperature (T)—are
commonly used to describe a gas. Ideal gases exhibit certain properties: The
volume of the gas molecules is negligible compared with that of the container that
holds them, they experience no electrical forces, and they undergo elastic
collisions. These three variables are related by the following equation:

PV = nRT

where n is the number of moles of gas and R is a constant (8.31 J/mol·K)

called the universal gas constant. This equation is known as the ideal

gas law.

This equation tells us that for a fixed volume of gas, an increase in P gives a
proportional increase in T. The pressure increases when the gas molecules strike
the walls of their container with more force, which occurs if they move more
rapidly.

Also, the equation

Kavg = kBT

tells us that the average translational kinetic energy of the gas molecules

is directly proportional to the absolute temperature of the sample.

From this we can find the root-mean-square speed of the gas molecule. mv^2 =
kBT

Because kB = R/NA and mNA = M (the mass of one mole of the molecules—the