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MIND MAP 4, SHARIFAH AZRA BT ABDUL KADIR - Coggle Diagram
MIND MAP 4
THERMAL PROPERTIES I
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Heat Capacity
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U = U(T,V)
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The heat capacity of such a system is defined as the amount of heat absorbed by a system per unit change in temperature
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Classical Results
The heat capacity at constant volume, CV as a function of temperature for solid
At room temperature, in most cases, the value of the heat capacity is 3Nk = 3R per mole = 25 J mol−1 deg−1. This result, derived from data is called the Dulong and Petit law.
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CV of free particles
Only have translational kinetic energy
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THERMAL PROPERTIES II
In quantum theory ,Thermal energy = total energy of the phonons in a equilibrium state
Debye's Model
Atoms are considered as harmonic oscillators that produce elastic waves with varying frequencies from ω = 0 to ωmax
The relations between the energy of a phonon E, the angular frequency ω and the wave vector q are
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This changes the expression for CV because each mode of oscillation contributes a frequency-dependent heat capacity and we now have to integrate over all ω
Debye temperature TD is defined
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Einstein's Model
Einstein assumed that the atoms are vibrating as harmonic oscillators, but instead of taking the classical expression for the energy of an oscillator
he assumed Planck’s (1990) quantization rule foreach oscillator (vibrating oscillators (atoms) in a solid have quantized energies)
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