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Unformatted text preview: CH301 Notes Chapter 10 SKIP SECTIONS 10.10-end Expansion Work against CHANGING External Pressure A REVERSIBLE, ISOTHERMAL expansion: We gradually reduce P ext from P initial to P final ; keep system at constant T (e.g., water bath) w = - nRT ln (V final / V initial ) whereR= 8.314 J/mol.K Comparing a REVERSIBLE vs. IRREVERSIBLE EXPANSION of a gas Reversibly : w = -nRT ln(V f /V i ) Irreversibly against constant external pressure: w = -P ext ' V if a vaccum , then w = 0 = Free expansion Main Concept: Work done by the system via is LARGER (the value is more negative) for a REVERSIBLE process!! Second Concept: An ISOTHERMAL expansion ( ' T = zero) ALSO has ' E = zero. This is because, for an ideal gas, internal energy is dependent ONLY on temperature, NOT P or V. Try it yourself: Two moles of an idea gas initially at 3atm and 183K are allowed to expand from 10L to 40L and a final pressure of 0.75 atm in two different ways: Find w , q and ' U. Path A. Isothermal, reversible expansion. Path B. Cooled at constant volume (10L) until P = 0.75 atm and then allowed to expand against a constant pressure of 0.75atm until V = 40L, T=183K. The Second Law of Thermodynamics “ In spontaneous changes the universe tends towards a state of greater entropy .” A mirror shatters when dropped - does not reform. Its easy to scramble an egg - impossible to reverse! Food dye when dropped into water disperses Spontaneous processes are those which occur by themselves . Think of a spontaneous process as being ‘feasable’. Spontaneity has nothing to do with speed . What is Entropy? Entropy (S) is disorder, but on a molecular level. A jumbled sock drawer is a metaphor for disorder! thermal disorder: Add heat energy to a sample: molecules can occupy a more varied combination of translational, vibrational and rotational energy levels. positional disorder: Allow a sample to expand or mix with another material: molecules can occupy more physical locations. Boltzmann: Formal Definition of Entropy on a Molecular level microstate : exact translational, vibrational, rotational, potential energies of each particle in a system -or- one set of the possible positional arrangements of each particle in a system macrostate: overall SUM of these energies, or, total number of possible positional arrangements S = k B lnW Note: if W = 1 S = 0 Add energy: W increases, so S increases B W = number of possible microstates of one molecule (positional and thermal -see later - we assume at T=0 you only have positional microstates) k B = Boltzman's constant = R/N B A = 1.381 x 10 J molecule K (NOTE: its PER MOLECULE! !) -23-1-1 Quantitative definition of Entropy...
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This note was uploaded on 02/12/2012 for the course CH 301 taught by Professor Fakhreddine/lyon during the Summer '07 term at University of Texas.
- Summer '07