CH 301 Ch 9 supplement Thermodynamics of Ideal Gases

# CH 301 Ch 9 supplement Thermodynamics of Ideal Gases -...

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Thermodynamics of Ideal Gases We consider adding heat energy to the simplest possible system: an ideal gas Heat Capacity of Ideal Gases From Chapter 5: <K.E. molar > = (3/2) RT NOTE: Use R = 8.314 J/K !!! If we add heat energy; and do NOT allow the gas to expand: ALL the energy goes into increasing the gas molecules’ <KE>, so the temperature increases. Energy required to change the temperature of 1 mole of an ideal gas by Δ T is 3/2R Δ T Energy required to change the temperature of 1 mole of an ideal gas by 1K is 3/2R MOLAR HEAT CAPACITY of an ideal gas heated at CONSTANT VOLUME: C V,m = 3/2R ALL energy goes into increasing the gas molecules’ <KE>, so temperature increases. What if gas EXPANDS? To get the same rise in T, we need MORE energy. SOME energy goes into increasing the gas molecules’ <KE>. SOME energy goes into doing expansion work. Work done by the gas as it expands: w = - P Δ V = - nR Δ T = - R Δ T (for 1 mole of gas) If Δ T = 1K then the work done by the gas is -R …..This much energy must also be supplied! Energy required to change the temperature of 1 mole of an ideal gas by 1K ( WITH expansion) is 3/2R + R MOLAR HEAT CAPACITY of an ideal gas heated at CONSTANT PRESSURE (i.e., it expands): C P,m = 3/2R + R which gives us C P,m = C V,m + R Comparing C P,m and C V,m : Due to the expansion work needed, you need MORE energy to get the

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## This note was uploaded on 12/11/2010 for the course CH 301 taught by Professor Fakhreddine/lyon during the Fall '07 term at University of Texas.

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CH 301 Ch 9 supplement Thermodynamics of Ideal Gases -...

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