Ideal Gases

January 23, 2013

Properties of a Gas

• Number of molecules (N) or moles (n)• Temperature (T) measured in K or °C– a measure of the average kinetic energy of the gas

• Volume (V) measured in m3

• Pressure (P) is the force per unit area the gas exerts on the walls of its container– measured in pascals (Pa), where 1 Pa = 1 N m–2

– atmospheric pressure (1 atm) = 101.3 kPa

STP (for gases)

• Standard Temperature and Pressure– 273 K (i.e. 0 °C)– 1 atm (i.e. 101.3 kPa)

Boyle’s Law

• a.k.a. Boyle-Mariotte Law

• In other words, PV is constant.

2211 VPVP

Boyle’s Law

Charles’s Law

• found by Charles and Guy-Lussac

• In other words, V and T are directly proportional.

2

2

1

1

T

V

T

V gas

water

mercury

h

Charles’s Law

Guy-Lussac’s Law

• In other words, P and T are directly proportional.

2

2

1

1

T

P

T

P

water

thermometer

heat

gas

pressure gauge

Gay-Lussac’s Law

2

2

1

1

T

P

T

P

Combined Gas Laws

2

22

1

11

T

VP

T

VP

nRTPV

Kinetic Model of Ideal Gases

• Molecules (and collisions) are perfectly elastic.• Molecules are spheres.• Molecules are identical.• There are no forces between molecules

(except when they collide).• Molecules are very small (i.e. total volume

much smaller than container volume).

Real Gases

• Gases do not behave as ideal gases in all conditions.

• At high pressures, or low temperatures, gases compress and behave more like liquids.

• However, most gases behave like real gases under “normal” conditions (e.g. STP).

Force/Pressure

• Two hollow cubes of side 0.25 cm with one face missing are placed together at the missing face. The air inside the solid formed is pumped out. What force is necessary to separate the cubes?

Molecules Have a Range of Speeds

• Average kinetic energy of molecules– Why?

• Root mean square (rms) speed.

Speed Distributions of Molecules• rms (root mean square) speed is a type of

average over all the molecules in the gas

Average vs. RMS Speed

• Four molecules have speeds of 300 m s-1, 350 m s-1, 380 m s-1, and 500 m s-1. Find the average speed and the root mean square speed.

Molecular Model of Gases

• A gas is compressed slowly by a piston. Explain why the temperature of the gas will stay the same.

• A gas is compressed rapidly by a piston. Explain why the temperature of the gas will increase.

• A gas expands isothermally. Explain from a molecular point of view why the pressure decreases.

• A gas is heated at constant pressure. Explain why the volume must increase as well.

A hair dryer consists of a coil that warms air and a fan that blows the warm air out. The coil generates thermal energy at a rate of 600 W.Take the density of air to be 1.25 kg m-3 and its specific heat capacity to be 990 J kg-1 K-1.The dryer takes air from a room at 20 C and delivers it at a temperature of 60 C. What mass of air flows through the dryer per second? What volume of air flows per second?