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Ideal Gas Law

Ideal Gas Law. Questions? (Doppler) Properties of Gases Ideal Gas Law Examples of Ideal Gas Law Kinetic Theory. Temperature and Gases. Gas Simplest phase – all kinetic energy. Kinetic energy reservoir - can finesse heat <- - > mechanical work. Properties of a Gas Pressure Volume

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Ideal Gas Law

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  1. Ideal Gas Law • Questions? (Doppler) • Properties of Gases • Ideal Gas Law • Examples of Ideal Gas Law • Kinetic Theory

  2. Temperature and Gases • Gas • Simplest phase – all kinetic energy. • Kinetic energy reservoir - can finesse heat <- - > mechanical work. • Properties of a Gas • Pressure • Volume • Temperature • Quantity • Properties are interrelated (animation) • Pressure vs. Volume (Boyle’s Law) P proportional to 1/V • Volume vs. Temperature (Charle’s law) V proportional to T • Pressure vs. Temperature (Gay-Lussac’s Law) P proportional to T • Pressure and volume vs. quantity PV proportional to n

  3. Ideal Gas Law • Ideal gas law combines Boyle’s Charles, Gay-Lussac’s PV = nRT • P in pascals (atmospheres) • V in m3 (liters) • T in K° (not C °) • n in moles • Definition of Mole n = mass/molecular mass (N2=28g/mol, O2= 32g/mol, etc.) • Two values for R 8.314 J/mol-K .0821 L-atm/mol-K

  4. Alternative Ideal Gas Law • Ideal Gas Law can also be written: PV = NkTPV = nRT • N = nNA (N number of molecules) • k= R/NA (NA Avagadro’s number) • P in pascals (no alternative units) • V in m3 • T in K° • Boltzman’sconstant • k = R/NA = 1.38e-12 J/K

  5. Celsius vs. Kelvin • When do you use Celsius? • When only relative changes matter • Thermal expansion • Specific Heat / Latent Heat • Heat Transfer Conduction • When do you use Kelvin? K° = C° + 273.15 • When absolute temperature matters • Ideal gas, Kinetic theory • Heat Transfer Radiation • 1st & 2nd Law Thermodynamics • Similar analogy for Gauge vs. Absolute Pressure

  6. Examples of Ideal Gas • Example 13-10 (volume 1 mole at STP) • n = 1 mole, P = 101.3 kPa V = 22.4 liters • Use both R’s • Example 13-11 (helium balloon) • Calculate volume from geometry • Calculate n from pressure and temperature • Calculate mass from n • Mass of air in room • Volume of room • Calculate n from pressure and temperature • Calculate mass from n

  7. More examples ideal gas • Example 13-13 (pressure variation with temp) • Problem 29 V2 = V1 (P1/P2) (T2/T1) • Problem 30 T2 = T1 (P2/P1) (V2/V1) • Problem 31 ρ = 32 x 10-3/22.4 x 10-3 • Problem 32 P2 = P1 (n2/n1) • Problem 33 • Problem 36 n2 = n1 (P2/P1) • Problem 39 P2 = P1 (V1/V2)(T2/T1)

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