L2 - Temperature Ideal Gas and Equipartition(2)

# L2 - Temperature Ideal Gas and Equipartition(2) - Lecture 2...

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Lecture 2 1) Temperature & Thermometers 2) Ideal Gas Law → Temperature ~ Kin. Energy 3) Equipartition Theorem Thermal physics - PH2103 Textbooks paragraphs: 1.1; 1.2; 1.3

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Temperature The definition of temperature is not easy. We will only provide a precise definition in a month.. From now on, we consider an operative definition of temperature, “ temperature is what you measure with a thermometer ”. In this lesson: 1) Empirical observations allowing to understand how a thermometer works 2) Ideal gas law the temperature of gases is related to their kinetic energy. 3) Equipartition theorem
Thermometry Three empirical observations allow for the functioning of thermometers system in thermal contact reach thermal equilibrium zeroth law of thermodynamics there are physical properties we can measure that change with temperature (e.g. volume, pressure, electrical resistance, …) We now have a look at these facts.

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Thermal equilibrium 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
Diffusive equilibrium Total volume: V = V 1 +V 2 Number of particles: N = N 1 +N 2 Q1: How many particles occupy volumes V 1 and V 2 after at long time ? Q2: What fixes how long we have to wait for this condition to occur? V 1 , N 1 (t= ) V 2 , N 2 (t= ) Since it is difficult to think about a flow of “energy”, let's consider a related example, diffusive equilibrium, that involves the flow of particles. We consider two volumes containing particles, separated by a closed valve . Closed valve no particle exchange no diffusive “contact” At time t = 0, we open the valve, and particles start being exchanged.

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Diffusive equilibrium Total volume: V = V 1 +V 2 Number of particles: N = N 1 +N 2 Q1: How many particles occupy volumes V 1 and V 2 after at long time ? Ans: Two volumes have the same density: Q2: What fixes how long we have to wait for this condition to occur? Ans: size of connecting tube i.e. properties of the diffusive contact V 1 , N 1 (t= ) V 2 , N 2 (t= ) equilibrium Relaxation time N 1 = N V 1 V N 2 = N V 2 V N 1 V 1 = N 2 V 2
Diffusive vs. thermal equilibrium Closed valve No thermal contact Open valve Flux of particles Flux of energy After some time Thermal contact After some time Equilibrium: same density Timescale Diffusive contact Equilibrium: same temperature Timescale Thermal contact Notes: 1) thermal contact does not imply physical contact 2) the “no thermal contact” condition is only ideal; one can only increase the timescale (chemical potential)

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What do we feel? Large flux of energy from the body to the metal We are not sensible to the temperature of an object, but to the flux of energy we exchange with than object.
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