hermdynamics: Gas Laws Resurces: Serway emperature & hermal Expansin: 10.1, 10.2, & 10.3 Ideal Gas Law: 10.4 & 10.5 AP Physics B Vides Physics B Lessn 25: Mechanical Equivalent f Heat Physics B Lessn 26: Specific and Latent Heat Physics B Lessn 27: Heat ransfer and hermal Expansin MI CurseWare 32: hermal Expansin 33: Ideal-Gas Law Heat & Gas he Macrscpic View We nw address the prperties f gas. Specifically: Pressure Vlume emperature Mass he relatinship that inter-relates these prperties is called an equatin f state. It is VERY cmplicated. Hwever, if we islate ur analysis t lw pressure, the inter-relatinships are simplified. his situatin is called an ideal gas. 1
Ideal Gases Ideal gasses d nt really exist, but mst gasses at 1 atmsphere f pressure behave like an ideal gas. he ideal gas simplificatin prvides regular mlecular interactins. he Peridic able All f the elements n the peridic table are referred t in terms f their atmic mass. he symbl u is dented as an atmic mass unit. Atmic # - # f prtns OR electrns 1 amu 1.66 x 10-27 kg r 1 amu 1 g / mle Atmic Mass - # f prtns + Neutrns 2
he Mle he wrd mle is derived frm Latin t mean heap r pile. It is basically a chemical cunting unit. Belw, what we have is called the Mle Rad Map and it summarizes what a mle equals. Atmic Mass frm P.. Avgadr s # 6.02 x 10 23 Particles 1 MOLE 22.4 Liters gas @ SP One mle f any gas at SP ccupies a vlume f 22.4 L SP Standard emperature and Pressure S 0 degrees Celsius r 273 Kelvin SP atmspheric pressure Example A flexible cntainer f Oxygen(O 2 ) has a vlume f 10.0 m 3 at SP. Find the # mles and mlecules that exist in the cntainer 3 1L 10m ( 3 1x10 m 1mle 22.4L )( ) 3 446.43 mles 23 6.02x10 mlecules 446.43mles( ) 1mle 2.68x10 26 mlecules 3
Factrs that effect a GAS 1. he quantity f a gas, n, in mles 2. he temperature f a gas,, in Kelvin (Celsius degrees + 273) 3. he pressure f a gas, P, in pascals 4. he vlume f a gas, V, in cubic meters Gas Law #1 Byles Law he pressure f a gas is inversely related t the vlume Mles/Mlecules and emperature are cnstant Istherm 1 k P α P V V k cnstant f prprtinality P V k k 4
Byles Law - Uses he bubbles exhaled by a scuba diver grw as they rise. Deep sea fish die when brught t the surface. Bends in humans. Gas Law #2 Charles Law he vlume f a gas is directly related t the temperature Pressure and Mles are cnstant V α V V k V k V V k 5
Charles Law - Uses Explains why tires shrink in cld weather and expand in ht weather. Why turkey thermmeters pp when turkey is dne. Why yu shuldn t verinflate yur life raft in trpical waters. Gas Law #3 Gay-Lussac s Law he pressure f a gas is directly related t the temperature Mles and Vlume are cnstant FYI: alchl by vlume (ABV) n alchlic beverage packaging is referred t as degrees Gay-Lussac P α P k P k P k P P 6
Vlume & emperature Gas Law #4 he Cmbined Gas Law Byle s Charles and Gay- Lussac s Law cmbined tgether. Mles are cnstant P V α k k k 7
Example Pure helium gas is admitted int a leak prf cylinder cntaining a mvable pistn. he initial vlume, pressure, and temperature f the gas are 15 L, 2.0 atm, and 300 K. If the vlume is decreased t 12 L and the pressure increased t 3.5 atm, find the final temperature f the gas. (12)(3.5)(300) (15)(2) 420 K he IDEAL Gas Law All factrs cntribute! In the previus examples, the cnstant, k, represented a specific factr(s) that were cnstant. hat is NO the case here, s we need a NEW cnstant. his is called, R, the universal gas cnstant. α n R cnstant f prprtinality J R Universal Gas Cnstant 8.31 ml K nr where, P: pressure (Pa) V: vlume (m 3 ) n: number f mles R: universal gas law cnstant 8.31 J/(ml K) : temperature (K) 8
Example A helium party balln, assumed t be a perfect sphere, has a radius f 18.0 cm. At rm temperature, (20 C), its internal pressure is 1.05 atm. Find the number f mles f helium in the balln and the mass f helium needed t inflate the balln t these values. 4 3 4 V sphere πr π (0.18) 3 3 20 + 273 293 K P 1. 05atm nr n 1.05 x 10 5 Pa R 3 0.0244 m 3 5 (1.05x10 )(0.0244) n (8.31)(293) 1.052 mles 4g m 1.052 ml 1ml 4.208 g Example Hw many mles f air are in an inflated basketball? Assume that the pressure in the ball is 171 kpa, the temperature is 20 C, and the diameter f the ball is 30.0 cm. 4 3 4 V ball πr π (0.18) 3 3 20 + 273 293 K P 171kPa nr n R 3 0.0141 m 3 3 (171x10 )(0.0141) n (8.31)(293) 0.990 mles 9
Avgadr s Law & Number Avagadr s Law: Equal vlumes f gas at the same temperature and pressure cntain the same numbers f mlecules. One mle quantities f all gases at SP cntain the same number f mlecules. Avgadr s Number (N 0 ) N 0 6.02 x 10 23 mlecules/ml N 0 6.02 x 10 23 ml -1 N N If the number f mlecules is knw (N) the number f mles (n) can be calculated by n dividing by Avgadr's number (N 0 ): 0 Avgadr s Law A flat tire takes up less space than an inflated tire. Lungs expand as they fill with air. Exhaling decreases the vlume f the lungs. A balln filled with helium weighs much less than an identical balln filled with air. Pressure and temperature held cnstant. Same number f mlecules, the helium is less dense. Wet air is less dense than mist air. 10
he IDEAL Gas Law & Avgadr's Law By cmbining the IDEAL gas law ( nr) and n N/N 0 we get an versin f the IDEAL Gas Law that is based n the number f mlecules in a gas. nr N R R N 0 N 0 Bltzmann' s Cnstant 1.38 x 10-23 J K Nk B where, P: pressure (Pa) V: vlume (m 3 ) k B : Bltzmann s cnstant 1.38 x 10-23 J/K : temperature (K) Summary he IDEAL Gas Laws n R (using mles, n) N k B (using mlecules, N) P: pressure (Pa) V: vlume (m 3 ) n: number f mles R: universal gas cnstant 8.31 J/(ml K) N: number f mlecules k B : Bltzman s cnstant 1.38 x 10-23 J/K : temperature (K) 11