240_l06 - Work and heat Chapter 2 of Atkins: The First Law:...

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Work and heat Sections 2.3-2.4 of Atkins (7th & 8th editions) Expansion Work General Expression for Work Free Expansion Expansion Against Constant Pressure Reversible Expansion Isothermal Reversible Expansion Heat Transactions Calorimetry Heat Capacity Chapter 2 of Atkins: The First Law: Concepts Last updated: Sept. 21, 2007; swapped positions of 17 & 18; no other changes

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Work and heat Must focus upon infinitessimal changes in state and energy, and be able to connect the contributions of small changes in heat and work to the total energy Work done on a system: dw Energy supplied as heat: dq dU ' dq % dw Expansion work: Work that leads to a change in volume - gas expanding, driving force against atmospheric pressure Examples: thermal decomposition of CaCO 3 combustion of octane
Expansion Work 1. Work required to move an object over distance dz against a force of opposing magnitude F : dw '& Fdz Negative sign: since the system moves against the opposing force F, there will be a decrease in the internal energy of the system 2. System: massless, frictionless, rigid, perfectly fitting piston of area A 3. Force on outer face of the piston: F = p ex A 4. Work done against external pressure: dw = - p ex Adz 5. Change in volume d V = Adz

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Expansion Work Work can now be written in terms of pressure and change in volume: w '& m V f V i p ex dV If we need to know the total work done expanding the volume of a system, we can integrate the above expression over the initial and final volumes # Force acting on the piston, p ex A , is the same as raising a weight as the system expands (e.g., F = mg ) # Compressing the system is analogous, excepting that V i > V f dw p ex dV If we have free expansion , there is no opposing force, despite increase (or decrease for compression) in volume. (e.g., expand into vacuum) w = 0
Types of Work There are various types of work from different sources which work much in the same way, resulting from the product of: an intensive factor (e.g., P ) x an extensive factor (e.g., V ) Type of work dw Comments Units Lifting - mg dh mg mass and gravity N dh is change in height m Expansion - p ex dV p ex is external pressure Pa dV is change in volume m 3 Surface expansion ( d F( is surface tension N m -1 d F is change in area m 2 Extension f dL f is the tension N dL is change of length m Electrical N dq N is electric potential V dq is change in charge C Generalized work: dw = - F dz where F is “generalized force” and dz is “generalized displacement”

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Expansion Against Constant Pressure During expansion, external pressure p ex is constant (e.g., atmosphere) w '& p ex m V f V i dV ' p ex ( V f & V i ) & If ) V = V f - V i , then the work can be written w p ex ) V The integral above is interpreted as area, as we watch work done by a gas expanding against a constant pressure The magnitude of work, * w * , is equal to the area beneath the line with p = p
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This note was uploaded on 10/24/2009 for the course CHEM 260 taught by Professor Staff during the Spring '08 term at University of Michigan.

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240_l06 - Work and heat Chapter 2 of Atkins: The First Law:...

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