L6 - Second-Law(1)

# L6 - Second-Law(1) - PH2103 Thermal Physics Lecture 6...

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PH2103 Thermal Physics Lecture 6: Second law of thermodynamics Massimo Pia Ciamarra [email protected] SPMS-PAP-03-14 Textbook paragraph: 2.1, 2.2, 2.3, 2.4 Discussion Forum

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1. Second law of thermodynamics Heat flows from hot to cold objects 2. Statistical approach Sequences & combinations Two-state paramagnet Harmonic oscillator - quantum mechanics Einstein Model of a Solid 3. Interacting systems Agenda
1. Second law of thermodynamics Heat flow from hot to cold objects

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Thermal equilibrium (lecture 2) When two objects interact thermally, energy flows from one system to the other until (thermal) equilibrium is attained . At this point, there is an observable which is the same for both systems. We call this observable temperature. Initial state After “some time” energy
Thermal equilibrium (lecture 4) To determine the relation between the heat flow Q and the temperature change T of a mass M we introduced the concept of heat capacity, C. We have found: Q = C T Conservation of energy tells us that the energy change (Q 1 ) of mass 1 is just the opposite of the energy change (Q 2 ) of mass 2: Q 1 +Q 2 = 0. We thus have, Q 1 = -Q 2 , and therefore C 1 (T eq -T 1 ) = -C 2 (T eq - T 2 ) From this relation we can extract T eq . Question: why the two objects reach thermal equilibrium? In principle, the final temperatures of the two objects could be different, e.g. T 1 final and T 2 final . In this case, the conservation of energy would read: C 1 (T 1 final -T 1 ) = -C 2 (T 2 final - T 2 )

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2 nd law of thermodynamics The fact that heat always flows from a hot to a cold object is not related to the conservation of energy. It is an independent observation, which is known as the second law of thermodynamics. Heat can never flow from a cold to an hot object without other changes, connected therewith , occurring at the same time. Second law of thermodynamics (Calusius statement) By clarifying the direction of the heat flow observed in nature, the second law of thermodynamics specifies the direction of time. We will see that the second law of thermodynamics admits many equivalent formulations. The second law of thermodynamics traces back to the development of thermodynamics, i.e. ~ 1850. It was formulated before the atomistic nature of matter was established without any doubt.
2. Statistical approach

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Statistical approach In this lesson, we try to understand the physical origin of the second law of thermodynamics using a statistical approach. 1) We use the fact that matter is made by particles 2) We consider that the number of particles is HUGE. The large number of particles leads to the developing of a statistical/combinatorial approach to the problem. We will see that all processes that conserve energy are possible. However, not all processes have the same probability to spontaneously occur.
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