PHYSICS 231 Lecture 24 Ideal gases PHY 231 1 Temperature scales Conversions Tcelsius Tkelvin 273 15 Tfahrenheit 9 5 Tcelcius 32 We will use Tkelvin If Tkelvin 0 0 the th atoms molecules t l l have no kinetic energy and every substance is a solid it is called the Absolute zero point Celsius Fahrenheit Kelvin PHY 231 2 Thermal expansion length L L Lo T surface f A A A Ao T T 2 2 volume V V V Vo T 3 3 L0 coefficient of linear expansion different for each material Some examples examples 24E 06 1 K Aluminum 1 2E 04 1 K Alcohol PHY 231 T T0 T T0 T 3 quiz extra credit A substance is measured to have a temperature of f 00C Celcius C l i s Which Whi h of f the th following f ll in is not n t true t a b c d The temperature in Kelvin is 273 15 K The temperature in Fahrenheit is 320F The atoms in the block are not moving at all The substance can be a gas gas a liquid or a solid PHY 231 4 Ideal Gas properties Collection of atoms molecules that Exert E no force f upon each h other h The energy of a system of two atoms molecules m m u cannot be reduced u by y bringing them close to each other Take no volume The volume taken by the atoms molecules is negligible compared to the volume they are sitting in PHY 231 5 Potential Energy Rmin 0 Emin R Ideal gas we are neglecting the potential energy between The atoms molecules Potential Energy Kinetic energy 0 R PHY 231 6 Number of particles mol 1 mol of particles 6 02 x 1023 particles A Avogadro s d number b NA 6 02x10 6 02 1023 particles ti l per moll It doesn t m matter what w kind of fp particles 1 mol is always NA particles PHY 231 7 What is the weight of 1 mol of atoms Number of protons Name Z X A molar l mass PHY 231 8 Weight of 1 mol of atoms 1 mol of atoms A gram A mass number Example 1 mol of Carbon 12 g 1 mol of Zinc 65 4 g What about molecules H2O 1 mol of water molecules 2x 1 g due to Hydrogen 1x 16 g due to Oxygen Total 18 g PHY 231 9 Example A cube of Silicon molar mass 28 1 g is 250 g A How much Silicon atoms are in the cube B What would be the mass for the same number of gold atoms molar mass 197 g A Total number of mol 250 28 1 8 90 mol 8 9 mol x 6 02x1023 particles 5 4x1024 atoms B 8 90 mol x 197 g 1 75x103 g PHY 231 10 question 1 1 mol of C02 has a larger mass than 1 mol of CH2 2 1 mol of CO2 contains more particles than 1 mol of CH2 a 1 is true and 2 is true b 1 is true and 2 is not true c 1 is not true and 2 is not true d 1 iss not true and 2 iss not true PHY 231 11 Boyle s Law P0 2V0 T0 P0 V0 T0 2P0 V0 T0 At constant temperature PHY 231 P 1 V 12 Charles law P0 2V0 2T0 P0 V0 T0 If you want to maintain a constant pressure the temperature must be increased linearly with the volume V T V T PHY 231 13 Gay Lussac s law P0 V0 T0 2P0 V0 2T0 If at constant volume the temperature is increased the pressure will increase by the same factor P T PHY 231 14 Boyle Charles Gay Lussac IDEAL GAS LAW PV T nR n number of particles in the gas mol R universal gas constant 8 31 J mol K P pressure Pa P P V volumn m3 T temperature p K If no molecules are extracted from or added to a system PV constant T PHY 231 P1V1 P2V2 T1 T2 15 Example An ideal gas occupies a volume of 1 0cm3 at 200C at 1 atm A How many molecules mo cu s are ar in n the th volume o um B If the pressure is reduced to 1 0x10 11 Pa while the temperature drops to 00C how many molecules remained in the volume A PV T nR so n PV TR R 8 31 J mol K T 200C 293K P 1atm 1 013x10 P 1atm 1 013x105 Pa V 1 0cm V 1 0cm3 1x10 66m3 n 4 2x10 5 mol n 4 2x10 5 NA 2 5x1019 molecules 11 Pa B T 0 T 00C 273K C 2 3K P P 1 0x10 1 0 10 11 P V V 1x10 1 10 66 m3 n 4 4x10 21 mol n 2 6x103 particles almost vacuum PHY 231 16 And another An airbubble has a volume of 1 50 cm3at 950 m depth T 7oC What is its volume when it reaches the surface water 1 0x103 kg m3 P950m m P0 watergh 1 013x105 1 0x103x950x9 81 9 42x106 Pa P1V1 P2V2 T1 T2 5 9 42 10 6 1 50 10 6 1 013 10 Vsurface 280 293 Vsurface 1 46x10 4 m3 146 cm3 PHY 231 17 Correlations A volume with dimensions LxWxH is kept under pressure P at temperature T A If the temperature is Raised by a factor of 2 2 and the height of the volume made 5 times smaller by what factor does the pressure change Use the fact PV T is constant if no gas is added leaked P1V1 T1 P2V2 T2 P1V1 T1 P2 V1 5 2T1 P2 5 2 P1 10P1 A factor of 10 10 Next quiz is something like this PHY 231 18 Diving Bell A cylindrical diving bell diameter 3m and 4m tall with an open bottom is submerged to a depth of 220m in the sea The surface temperature is 250C and at 220m T 50C The density of sea water is 1025 kg m3 How high does the sea water rise in the bell when it is submerged Consider the air in the bell Psurf 1 0x105Pa Vsurf r2h 28 3m3 Tsurf 25 273 298K Psub P0 wg depth 2 3x106Pa Vsub Tsub 5 273 278K Next use PV T constant PsurfVsurf Tsurf PsubVsub Tsub plug in n the numbers and f find nd Vsub 1 15m3 this is the amount of volume taken by the air left Vtaken by water 28 3 1 15 27 15m3 r2h h 27 15 r2 3 8m h 27 15 r 3 8m rise of water level in bell bell PHY 231 19 A small matter of definition Ideal gas law PV T nR PV T N NA R PV T N N n number of mols N number um of fm molecules u NA number of molecules in 1 mol Rewrite ideal gas law PV T NkB where kB R NA 1 38x10 23 …
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