Gas Laws For “ideal” gases

Boyle’s Law For a fixed mass of gas at a fixed temperature, the product of pressure and volume is a constant p x V = constant

Volume of Gas Pressure 0.1m Nm -2 PV = Nm

Volume m 3 Pressure 2 x 10 5 Nm -2 Volume =0.05m 3 PV= 10 4 Nm

P = 3x10 5 Nm -2 V=0.033m 3 PV = 10 4 Nm

P= 4x10 5 Nm -2 V=.025m 3 PV= 10 4 Nm

Volume of the gas m 3 Pressure of the gas Nm -2

Volume of the gas Pressure of the gas

Volume of the gas m 3 Pressure of the gas Nm -2 Volume of the gas m 3 1/Pressure of the gas m 2 N -1 P  1/V

Verifying Boyle’s Law Bourdon Guage Air from footpump valve Fixed mass of air Scale gives volume of trapped air

Experimental detail 1.The gas under investigation is trapped above the oil in a glass tube. This ensures a fixed mass of gas. 2.The volume V of air is read directly from the scale. The pressure is recorded on the bourdon guage. 3.It is compressed using a footpump to increase the pressure above the oil in the reservoir. The pressure(p) is increased in equal stages alowing pairs of values of p and V to be measured. 4.Compressing the air warms it slightly so it is given time to cool, indicated by a steady volume reading between each reading. 5.A graph of V against 1/p is drawn which is a straight line through the origin.

Two other gas laws Charles’ Law For a fixed mass of gas at constant pressure, the volume is directly proportional to the Kelvin temperature.

Capiliary tube of uniform cross section Mercury bead Fixed mass of gas thermometer As the water is heated the volume of the trapped gas increases at constant pressue. It is found that V  T

The pressure law For a fixed mass of gas at a fixed volume, the pressure is directly proportional to the temperature measured in kelvins. PVPV

Temperature/C Volume m When the line is extrapolated back to the x axis, it meets it at just about C. This led to the idea of an absolute zero of temperature.. Of course no real gas could get to this temperature as it would change state before it did! Remember in calculations in thermal physics always use Kelvins for temperature

At constant TpV = a constantor At constant pV/T= a constantor VTVT At constant vp/T= a constantor pTpT

Combining the 3 laws Fixed mass of gas Same mas of gas P1V1T1P1V1T1 P2V2T2P2V2T2 The three laws can be combined to give a rule for a fixed mass of gas

Question A gas which can be considered ideal has a volume of 100cm 3 at 2.00Pa and 27C. What is its volume at 5.00Pa and 60 C p 1 = 2.00 x 10 5 Pa P 2 = 5.00 x 10 5 Pa V 1 = 100cm 2 V 2 = V 2 T 1 = 300K T 2 = 333K

Ideal Gases No gas obeys the gas laws exactly. They provide a fairly accurate description of the way the real gases work. This is because in real gases there are often forces between molecules. To overcome this difficulty the idea of an ideal (perfect) gas was introduced.

Assumptions For Ideal Gases 1.Intermolecular forces are negligible except during collisions. 2.The volume of the molecules themselves can be neglected compared with the volume occupied by the gas. 3.The time for any collision is negligible compared with the time spent between collisions. 4.Between collisions molecules move with uniform velocity. These conditions imply that all of the internal energy of the gas is kinetic.

The ideal gas equation The combination of the gas laws tell us that Is a constant for a fixed mass of gas. Ie that In fact k is found to be equal to the product of two previously know values k= n x R. n is the number of moles of gas present in the fixed mass of gas. R is called the universal molar gas constant (= 8.31JK -1 mol -1 )

P is the pressure in Nm -2 V is the volume m 3 n is the number of moles of gas present T is the temperature of the gas in K

A word about moles A mole of gas is the quantity of gas which contains 6 x molecules: Hydrogen gas H 2 2g Oxygen gas O 2 32g Nitrogen gas N 2 28g You do not need to know these values and will be told something like…. 0.2 moles of gas….. etc

Ideal gases an ideal gas obeys PV=nRT exactly. No such real gas exists. The internal energy on an ideal gas is entirely kinetic and depends only on its temperature. (ie. There are no forces acting at a distance between molecules in the gas) The behaviour of real gases approximates PV=nRT at low pressures and temperatures well above the point at which they liquefy