# Lect03 - Lecture 3 Classical Illustrations of Macroscopic...

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Physics 213: Lecture 3, Pg 1 Lecture 3 Lecture 3 Classical Illustrations Classical Illustrations of Macroscopic Thermal Effects of Macroscopic Thermal Effects Heat capacity of solids & liquids Heat capacity of solids & liquids Thermal diffusion Thermal diffusion Thermal conductivity Thermal conductivity Thermal expansion Thermal expansion Reference for Lecture 4: Elements Ch 5 References for this Lecture: Elements Ch 3,4A-C

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Physics 213: Lecture 3, Pg 2 Last time: Heat capacity Last time: Heat capacity The heat capacity of a substance can be determined at constant volume (C V ) or constant pressure (C P ). Both depend on the material and often on T. Q C (for small T) T C Heat capacity --- heat energy required to raise the temperature of a sample by 1K (=1ºC) Depends on amount of material standard Units: J / K Q = U + W by (1 st Law of Thermodynamics) If we add heat to a system, there are two general destinations* for the energy: it will ‘heat up’ the system, i.e., raise T it can make the system do work (usually positive) on the surroundings * If the system has internal ‘parts’, it could also add energy to them (cf. winding a clock).
Physics 213: Lecture 3, Pg 3 High-T heat capacity of a solid High-T heat capacity of a solid Vibration of atom in solid atoms are like little balls connected by springs (interatomic forces); they have normal modes of vibration like harmonic oscillators, with kinetic + potential energy. C = 3Nk = 3 nR U thermal = 3NkT = nRT (3N normal modes) (often works near room temperature and above) Equipartition Theorem, applies at high enough T, so each normal mode has a thermal energy of kT (KE +PE) For N atoms in the solid, the total vibrational energy is: For solids (and usually liquids): V doesn’t change much, so C V ~ C P (since very little energy goes into work pdV). Often substantial T-dependence of C V (T). Lots of energy goes into potential forms.

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Physics 213: Lecture 3, Pg 4 Heat capacity and ‘specific heat’ of substances Heat capacity and ‘specific heat’ of substances m C c = n C c mol = For solids (and usually liquids), the volume doesn’t change much , so C V ~ C P (since very little energy goes into work). T Q C = Heat capacity --- heat energy required to raise the temperature of a sample by 1K (=1ºC) Depends on amount of material Units: J / K Specific heat --- heat capacity normalized to a standard mass or to the number of particles: Depends on material properties only normalize to mass (solids or liquids) Units: J / kg - K or normalize to number of moles “molar specific heat” Units: J / mol K Question: Which has the higher c, aluminum or lead?
Physics 213: Lecture 3, Pg 5 Exercise 1: Rocket heat shields This false-color view of Titan (moon of Saturn) is a composite of images captured by Cassini's infrared

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Lect03 - Lecture 3 Classical Illustrations of Macroscopic...

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