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- The temperature in
**Kelvin**is 273.15 + the temperature in Celsius. Henceforth we will assume that*all*temperatures will be in Kelvin.Note that since Celsius and Kelvin temperatures differ by an additive constant, a difference in temperatures ΔT is numerically the same in either unit.

**Avogadro's number**N_{A}= 6.022 * 10^{23}, is the number of atoms or molecules in a**mole**. We will assume that we are working with numbers of atoms or molecules on the order of N_{A}.- The heat required to change the temperature of an object is
Q = m c ΔT = C ΔT,

where c is the**specific heat**of the substance and C is the**heat capacity**of the object.When the volume is constant, we often write

ΔQ = n c

where n is the number of moles and c_{v}ΔT_{v}is the**molar specific heat at constant volume**.Likewise, when the pressure is constant, we often write

ΔQ = n c

where c_{p}ΔT,_{p}is the**molar specific heat at constant pressure**. - The heat required to change the
**phase**of a substance isQ = m L,

where L is the**latent heat**(L_{f}of fusion or L_{v}of vaporization).c(water) = 1 cal/gK (1 **cal (calorie)**= 4.186 J)L _{f}(water) = 80 cal/gc(ice) = 0.51 cal/gK L _{v}(water) = 540 cal/gc(water vapor) = 0.48 cal/gK (at constant pressure) - The thermal power of
**conduction**isdQ/dt = k A dT/dx,

where k is the**thermal conductivity**, A is the cross-sectional area through which heat is being transferred and dT/dx is the temperature gradient. This expression is isomorphic to Ohm's law with the substitutions:- dQ/dt → I
- dT → ΔV
- dx / (k A) → R

- The thermal power of
**radiation**isdQ/dt = σ A e T

where σ is the^{4},**Stefan-Boltzmann constant**(5.67 * 10^{-8}W / (m^{2}K^{4})) and e is the**emissivity**, equal to the fraction of incoming radiation which is absorbed. An emissivity of 1 corresponds to a black body.This result follows from integrating the black body distribution from λ = 0 to ∞. That integral is the power per unit area, and e < 1 if the source is not a black body. The Stefan-Boltzmann constant is the coefficient of T

^{4}in the integral, equal to2 k

_{B}^{4}π^{5}/ (15 c^{2}h^{3}). - The
**coefficient of linear expansion**α is defined via a Taylor series expansion of the length as a function of temperature, analogously to the temperature coefficient of resistivity. - For ΔT << 1, the
**volume coefficient of expansion**is β = 3 α (use the binomial expansion).

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©2012, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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