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Thermal Properties - Coggle Diagram
Thermal Properties
Thermal Properties I
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Heat Capacity
- first law of thermodynamics
- Increase energy, dU of a system equal to amount of heat absorbed by the system, dQ, minus amount work dine by the system
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Definition:
- amount of heat absorbed by system per unit charge in temperature
Constant volume
Constant pressure
Classical Result
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- room temperature, value of heat capacity is 3Nk=3R per mole = 25 J mol-1 deg-1
- Dulong and Petit law
- lower temperature, heat capacity drops markedly ad approach zero, T^3
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Thermal Properties II
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Debye Model
Developed more sophisticated treatment of atomic vibration solids:
- atom consider as harmonic oscillators that produce elastic waves varying frequency
- treat solid as continuous elastic medium
- 3N normal modes oscillations
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Debye temperature:
Heat Capacity:
At high Temperature
- x is very small throughout the range of the intergral
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- The classical Dulong-Petit result
At low temperature
- only long wavelength acoustic modes are thermally excited
- the energy short wavelength modes are too high to be populated significant
- approximately Xd=Td/T
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Why Debye model better at low temperature than Einstein model?
- gives better representation for the very low energy vibrations
- vibrations matter most
Limits of the Debye model: