PRESSURE, HEAT AND GAS LAWS

INTRODUCTION

Gas is one of the three physical states of matter and is unlike liquids and solids in that a gas will tend to expand to occupy all the space available to it.

Gas is a substance that expands easily to fill any small empty container. It is readily compressible

Liquid flows freely in response to unbalanced forces but maintains a free upper surfaces. Compresses only slightly

Solids resists change of shape and volume. May resist large unbalanced forces without yielding. When yielding it deforms and may often break

We are only interested in the gross or bulk properties of gases.

Mass of atmosphere is 56 trillion tons

1 cubic centimeter of air at sea level pressure has 25 billion billion molecules and if you were to evacuate a container with a volume of one cubic cm and seal it off except for a small hole that will admit one billion molecules per second it will take 800 years to fill.

Two factors, temperature and density largely determine the pressure a gas will exert.

DALTON'S LAW OF PARTIAL PRESSURES

The pressure P exerted by a mixture of ideal gases in a given volume V at absolute temperature T is equal to the sum of the pressures Pi which would be exerted by each respective individual gas if it alone occupied volume v at the same temperature so that (P1 + P2 + P3+....Pi) V= (n1 + n2 + n3 + ...ni) RT ******** where n is the number of moles in each gas and R is the universal gas constant with the value of 8.314 x 10 to the 7th mole K

LAW OF GUY-LUSSAC

Relates temperature and volume with pressure constant. Volume of a gas increases with increase f temperature at rate of 1/273 of volume at 0 C with each l deg. C increase in temperature

V= (1+ 1/273 t)

BOYLE'S LAW

Pressure and volume are inversely related such that if temperature remains constant a 2fold pressure increase results in a decrease to one half the original volume, 3 fold pressure increase decreases volume to one third. Therefore the product of pressure and volume is constant. pV=K

CHARLES LAW

If volume is constant the pressure of a gas is directly related to temperature. Pressure increases with increase in temperature at rate of 1/273 of value at 0 C for each 1deg. C change in temp. p=po +1/273 tpo where p is pressure po is pressure at 0 C and t is change in temp in celsius. Another version of the equation is p=po ( 1+ 1/273 t)

UNIVERSAL GAS LAW (EQUATION OF STATE)

-pressure of a gas is equal to its temperature times its density

times a constant

-pressure is proportional to temperature and density of a gas

IDEAL GAS LAW

Equation is as follows with out atmosphere M=29, P is in mb, p in kg per cubic m and T in absolute scale

P=(2.87)pT or P=(2.87) m/V T

GAS LAWS

-if density held constant a rise in tempeature is accompanied by an increase in pressure

-if the temperature is held constant an increase in pressure is accompanied by an increase in density

-at constant pressure a rise in temperature means a decrease in density

ATMOSPHERIC PRESSURE

Pressure is essentially force exerted per unit area

In the case of the atmosphere the pressure is equal in all directions

Atmospheric pressure is primarily due to the force of gravity

-which compresses the molecules near the surface

-the pressure itself is caused by the impact of the air molecules and is related to the mass of the molecules and the speed with which they are moving (temperature) and gravity

-usually air pressure is described as the weight per unit area of the column of air above that location. Weight is the force exerted by gravity on a mass of air such that

weight= mass x gravity

Atmosphere is compressible therefore both pressure and density

are highest at the surface of the earth

-density at sea level is 1.23 grams per liter

At sea level a gas molecule travels .000025 cm between collisions;

at 50 km it travels 9.8 cm and at 100 km 32.3 meters

Atmospheric pressure always decreases with altitude

-near sea level drops about 10 mb per l00 meters

or drops 1/30th of its original value for each 300 meter rise

- at 10 km is 264 mb; at 20 km is 55.21 mb; at 30 km is 11.52 mb at 40 km is 2.78 mb; at 50 km is .93 mb

Highest recorded pressure was 1084 mb in Siberia, while lowest

was 870 mb in a typhoon

Practical Aspects

-cabins of jets are pressurized because otherwise the paying customers would die for lack of oxygen

-in the movies nobody is ever sucked out of airplanes, rather they are pushed out by the force of molecules

PRESSURE UNITS AND MEASUREMENT

There are a number of different ways of measuring pressure

-l4.7 lb/ square inch

-29.92 inches of mercury

-760 mm of mercury

-l0l3.25 millibars

A bar is a force of 100,000 newtons acting on a surface area of

one square meter

-one newton is the amount of force required to move an object

with a mass of l kg so that it accelerates at l m/sec/sec

- one bar is equal to 1000 millibars

l pascal is the force of one newton acting on a surface area of one square meter. One hundred pascals equals one millibar therefore

1013.25 mb is equal to 101.325 pascals

The barometer is the device which is used to measure atmospheric pressure

-therefore atmospheric pressure is sometimes refereed to as barometric pressure

-the mercury barometer was invented by Torricelli in l643

-Torricelli was a student of Galileo

-mercury was used due to its density and the fact that it does not evaporate

-a water barometer would have to be nearly 34 feet high (note that there is one in the atrium of the Durham Science Center). The blue color comes from copper sulfate which prevents algal growth.

Aneroid barometer

-the common circular one found on the walls of many homes or on desktops

-contains no fluid

-small flexible metal box which is partly evacuated of air

-size of metal box is calibrated to represent different pressures

-size changes are amplified and fed to lever

altimeter is essentially a type of aneroid barometer

Reduction of Pressure to Sea Level

-pressure observations must be reduced to a common reference level

-reduction to sea level means computing the pressure that would exist at the station if the elevation were truly at sea level

-done by making station corrections including temperature and

gravity

-correction done by means of hypsometric formula and standard

atmosphere