Lect02 - Physics 213 . Lecture 2 Ideal Gases: Energy, Work...

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Physics 213: Lecture 2, Pg 1 Ideal Gases: Energy, Work and Heat Ideal Gases: Energy, Work and Heat Thermal reservoir Physics 213 Physics 213 … Lecture 2 Lecture 2 http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm increasing T Volume Pressure c First Law of Thermodynamics - internal energy - work and heat References for Lecture 3 and 4: Elements Ch 3,4A-C and 5 Topics
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Physics 213: Lecture 2, Pg 2 Last time: The Ideal Gas Law Last time: The Ideal Gas Law c Together give us the Ideal Gas Law : 2 3 TRANS N p KE V = ( 29 2 2 2 3 1 2 2 TRANS x y z KE m v v v kT = + + = NkT pV = c The Pressure-Energy relation we derived: c Plus the Equipartition Principle (1/2 kT per quadratic DOF): Later, we will find that this law follows very directly from the definitions of an ideal gas and of T
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Physics 213: Lecture 2, Pg 3 c For an ideal gas at constant T, p is inversely proportional to the volume: Ideal gas p Ideal gas p -V, p V, p -T diagrams T diagrams V NkT p = increasing T Volume Pressure Real gases may obey more complicated equations of state, but still two of these variables determine the third. Ordinary gases are often quite close to ideal. p vs. V at various constant T’s ISOTHERMS 0 Temperature 0 “Constant Volume Gas Thermometer” Pressure drops toward zero at absolute zero temperature as the thermal kinetic energy of the molecules vanishes. p vs. T at constant V This relation holds Independently of the internal modes of the molecules.
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Physics 213: Lecture 2, Pg 4
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Physics 213: Lecture 2, Pg 5 Consider a fixed volume of an ideal gas. If you double either T or N , p goes up a factor of 2. ( pV = NkT ) If you double N , how many times as often will a particular atom hit the container walls? (A) × 1 (B) × 1.4 (C) × 2 (D) × 4 ACT 1: Ideal gas behavior
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Physics 213: Lecture 2, Pg 6 Dalton’s Law of Partial Pressures for ideal gases If a gas has multiple components (e.g., 78% N 2 , 21% O 2 , etc.), the total pressure is the sum of the individual partial pressures: p total = p 1 + p 2 + p 3 +… Example: Since air is 78% N 2 (by number , not by weight), the partial pressure of the nitrogen component is just 0.78 x 1 Atm. To get pV=NkT, we never used that the molecules were all of the same type. Equipartition makes the contribution of a molecule to the pressure independent of its mass. All that matters is how many molecules there are.
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Physics 213: Lecture 2, Pg 7 c “Classical” means Equipartition Principle applies: in thermal equilibrium, each molecule has average energy ½ kT per quadratic mode Internal Energy of a Internal Energy of a Classical Classical ideal gas ideal gas And we define (for 213) And we define (for 213) α α -ideal gases ideal gases V p T k N U α = α = c For a classical ideal gas: ( α depends on the type of molecule ) At room temperature, for most gases : T k N U 2 3 = monatomic gas (He, Ne, Ar, …) 3 translational modes (x, y, z) T k N U 2 5 = diatomic rigid molecules (N 2 , O 2 , CO, …) 3 translational modes (x, y, z)
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Lect02 - Physics 213 . Lecture 2 Ideal Gases: Energy, Work...

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