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Phys7B_03

# Phys7B_03 - Physics 7B Week 3 19.5 Macroscopic description...

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Physics 7B: Week 3 ! 19.5: Macroscopic description of ideal gas ! ! ! 20.3: Latent heat ! 20.4: Work and Heat ! 20.5: 1 st law of thermodynamics Physics 7B: Week 3 Slide 2 An Ideal Gas " For gases, the interatomic forces within the gas are very weak " We can imagine these forces to be nonexistent " Note that there is no equilibrium separation for the atoms " Thus, no “standard” volume at a given temperature

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Physics 7B: Week 3 Slide 3 Ideal Gas, cont " For a gas, the volume is entirely determined by the container holding the gas " Equations involving gases will contain the volume, V , as a variable " This is instead of focusing on ! V Physics 7B: Week 3 Slide 4 Gas: Equation of State " It is useful to know how the V olume, P ressure and T emperature of the gas of mass m are related " The equation that interrelates these quantities is called the equation of state " These are generally quite complicated " If the gas is maintained at a low pressure (or low density), the equation of state becomes much easier " This type of a low density gas is commonly referred to as an ideal gas
Physics 7B: Week 3 Slide 5 The Mole " The amount of gas in a given volume is conveniently expressed in terms of the number of moles " One mole of any substance is that amount of the substance that contains Avogadro’s number of constituent particles " Avogadro’s number N A = 6.022 x 10 23 =1mole " The constituent particles can be atoms or molecules Physics 7B: Week 3 Slide 6 Moles, cont " The number of moles can be determined from the mass of the substance: n = m / M " M is the molar mass (atomic mass, unit [u]) of the substance " m is the mass of the sample " n is the number of moles " What is the mass of 1 mol of water? " 1mole = N A = 6.022 x 10 23 " Water H 2 O " M=18u " Oxygen 16u, Hydrogen 1u. " 1u=1.66 10 -24 g;

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Physics 7B: Week 3 Slide 7 Gas Laws: Boyle’s law " When a gas is kept at a constant temperature, its pressure is inversely proportional to its volume " Boyle’s law Physics 7B: Week 3 Slide 8 Gas Laws: Gay-Lussac’s law " When a gas is kept at a constant pressure, its volume is directly proportional to its temperature " Charles and Gay-Lussac’s law:
Physics 7B: Week 3 Slide 9 Ideal Gas Law " The equation of state for an ideal gas combines and summarizes the other gas laws PV = nRT " This is known as the ideal gas law " R is a constant, called the Universal Gas Constant " R = 8.314 J/(mol K) = 0.08214 L atm/(mol K) # 1 mole of any gas at atmospheric pressure and at 0 o C is 22.4 L Physics 7B: Week 3 Slide 10 Ideal Gas Law, cont " The ideal gas law is often expressed in terms of the total number of molecules, N , present in the sample " PV = nRT = ( N / N A ) RT = Nk B T " k B is Boltzmann’s constant (R/N A ) " k B = 1.38 x 10 -23 J/K " It is common to call P , V , and T the thermodynamic variables of an ideal gas

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Physics 7B: Week 3 Slide 11 Atmospheric pressure " Standard atmosphere (symbol: atm) is a unit of pressure and is defined as being
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Phys7B_03 - Physics 7B Week 3 19.5 Macroscopic description...

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