1 / 10

Chapter-19

Chapter-19. The Kinetic Theory of Gases. Chapter-19 The Kinetic Theory of Gases. Topics to be covered: Ideal gas law Internal energy of an ideal gas Distribution of speeds among the atoms in a gas Specific heat under constant volume Specific heat under constant volume.

ismael
Download Presentation

Chapter-19

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter-19 The Kinetic Theory of Gases

  2. Chapter-19 The Kinetic Theory of Gases • Topics to be covered: • Ideal gas law • Internal energy of an ideal gas • Distribution of speeds among the atoms in a gas • Specific heat under constant volume • Specific heat under constant volume. • Adiabatic expansion of an ideal gas

  3. Ch 19-2, 3 Avogadro Number • M= m NA ; N= nNA; Msamp=n M NA • Ideal gas law: An ideal gas obey the law pV=nRT where R=8.31 J/mol.K • Boltzman constant k k = R/NA • pV=nRT=NkT • Kinetic Theory of gases: Relates motion of atoms to the volume, pressure and temperature. • Mole: one mole is number of atoms in a 12 g sample of carbon-12 • Avogadro Number: one mole contains Avogadro number NA of atoms NA = 6.02 x 1023 atoms/mol • n= number of moles • N= number of molecules • M= Molar mass of a substance • Msamp= mass of a sample then

  4. Ch 19-3 Ideal Gas and work done by the ideal gas • Work done by an ideal gas at constant Temperature (Isothermal expansion ): An ideal gas is allowed to expand from initial state pi,Vi to pf,Vf at constant T, the work W is: W=VfVipdV=VfVi (nRT/V)dV= W=nRTln(Vf/Vi) • Work done by an ideal gas at constant volume: W=VfVipdV=0 and Eint=Q • Work done by an ideal gas at constant pressure W=p(Vf-Vi)=pV=nRT

  5. Ch 19-4,5 Pressure, Temperature, RMS Speed and Translational Kinetic Energy • Pressure p relation to root-mean -square speed vrms and temperature T • P=(nM vrms 2)/3V but pV=nRT then • Vrms =  [(3RT)/M] • Translational Kinetic Energy K: Average translational kinetic energy of a molecule Kavg=(mv2/2)avg=m(vrms2)/2 • Kavg=m(vrms2)/2=(m/2)[3RT/M] =(3/2)(m/M)RT=(3/2)(R/NA)T Kavg=(3/2)(R/NA)T=(3/2)kT

  6. Ch 19-8 The Molar Specific Heats of an Ideal Gas • Internal Energy Eint: Ideal gas is monatomic and its Eint is sum of translational kinetic energies of its atom. For a sample containing n moles, its internal energy Eint: Eint=nNAKavg=nNA(3/2)kT= (3/2)n(NAk)T Eint= (3/2)nRT • Molar Specific Heat at Constant Volume For an ideal gas process at constant volume pi,Ti increases to pf,Tf and heatabsorbed QV=nCVT and W=0. Then Eint= (3/2)nRT= Q=nCVT CV= 3R/2 Where CV is molar specific heat at constant volume

  7. Ch 19-8 The Molar Specific Heats of an Ideal Gas • Cp :Molar Specific Heat at Constant Pressure: For an ideal gas process at constant pressure Vi,Ti increases to Vf,Tf and heatabsorbed QP=nCpTand W=pV= nR T. Then Eint= (3/2)nRT= Q-W =nCpT- nRT. Cp= 3R/2+R=5R/2 Where Cp is molar specific heat at constant pressure • Cp= CV + R; specic heat ration = Cp/ CV For monatomic gas Cp= 5R/2 ; CV= 3R/2 and = Cp/ CV = 5/3

  8. Ch 19-11 The Adiabatic Expansion of an Ideal Gas • Adiabatic process:In anadiabatic expansion of an ideal gas no heat enters or leaves the system i.e. Q=0 • P, V and T are related to the initial and final states with the following relations: PiVi= PfVf TiVi-1 = TfVf-1 • Also T/( -1) V =constant then piTi(-1)/ = pfTf(-1)/

  9. Ch 19-11 The Adiabatic Expansion of an Ideal Gas Free Expansion • Free Expansion of an ideal gas- • An ideal gas expands in an adiabatic process such that no work is done on or by the gas and no change in the internal energy of the system i.e. Ti=Tf • Also in this adiabatic process since ( pV=nRT), piVi=pfVf ( notPiVi= PfVf)

  10. Suggested problemsChapter 19

More Related