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# Lecture16A - The Third Law of Thermodynamics(Chapter 21...

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Lecture 16 1 The Third Law of Thermodynamics (Chapter 21) Since entropy is related to motion/disorder (and is sometimes induced by heat), it will be useful to explore this connection. As we have seen: dU=TdS-PdV ( 29 and formally we can write , V V T C U U dU V T dT dV T V = + 1 2 3 equating: 1 V T V T V T U TdS PdV C dT dV V U TdS C dT P dV V C U dS dT P dV T T V - = + = + + = + + Note: , 1 and V V T T C S T T U S P T V V = + =

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Lecture 16 2 At constant V: V C dS dT T = This is quite useful as heat capacities are not hard to come by. 2 1 2 1 T V T C S S S dT T = - = By the same logic as above, you can easily show 1 and P P T T C S S H V T T P T P = = - Start from P P T T H H H dH TdS VdP dT dP C dT dP T P P = + = + = + ( 29 2 1 2 1 at constant P: and T P P T C T C dS dT S S S dT T T = = - = Let’s think for a moment. At T=0K is there any thermal motion? NO! Is there any motion at all? Yes, vibrational zero point motion!
Lecture 16 3 If there is no thermal motion, then what is S at 0 K? 3 rd Law of Thermodynamics : All substances have S>0 for T>0 and as T 0, S 0 for pure crystalline materials.

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Lecture16A - The Third Law of Thermodynamics(Chapter 21...

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