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# lecture25 - 11/18/10 Phys 2101 Gabriela Gonzlez pV=nRT 2 1...

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11/18/10 1 Phys 2101 Gabriela González 2 pV=nRT

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11/18/10 2 3 The average translational kinetic energy of molecules in a gas is related only to temperature (not pressure, or volume). The internal energy of a gas is the total kinetic energy, also related just to temperature. For a monoatomic, ideal gas, E int = nN A K avg = (3/2) N k T = (3/2) nRT 4 We defined heat capacity C and specific heat c (heat capacity per mass) as: Q = C Δ T = c m Δ T For water, c = 1cal/g o C = 4187 J/kg K The molar specific heat is the heat capacity per mole. However, the amount of heat needed to raise the temperature of 1 mole by 1 kelvin depends on whether we perform the operation at constant pressure or at constant volume: Q = n C P Δ T or Q = n C V Δ T In both cases, Q= Δ E int +W: Δ E int is the same, but W is not!
11/18/10 3 5 Consider a process at constant volume, raising the temperature by Δ T . Q = n C V Δ T Q= Δ E int + W W = 0 ! Q = Δ E int = (3/2) nR Δ T = n C V Δ T C V = (3/2)R = 12.5 J/molK E int = n C V T E int = (3/2)nRT 6 Consider a process at constant pressure, raising the temperature by Δ T. Q = n C P Δ T Q= Δ E int + W W = p Δ V = n R Δ T Δ E int = (3/2) nR Δ T Q = Δ E int + W = (5/2) nR Δ T C P = (5/2)R = C V + R pV=nRT

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11/18/10 4 7 For any process (1, 2, 3 or 4): pV = n R T Δ E int = Q – W E int = (3/2) n R T = n C V T Also, C P = C V + R ; C V =(3/2)R Constant volume (4): W=0, Q = n C V Δ T Δ E int = n C V Δ T Constant pressure (1): W= p Δ V = nR Δ T Q = n C P Δ T Δ E int = n C V Δ T Constant temperature (2): W = nRT ln (V f /V i ), Δ E int = 0 Q = W = nRT ln (V f /V i ) True for monoatomic gases, but not for others!? 8
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## This note was uploaded on 12/01/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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lecture25 - 11/18/10 Phys 2101 Gabriela Gonzlez pV=nRT 2 1...

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