Contents

heat and thermal energy, agitation

conduction (convection)

simplest case we can think of: slender rod

thermal energy density e(x,t)

units Joule (J) examples: mgh, 1Ws, 1 Amp across 1 Volt for 1 sec

what happens in a chunk over time

conservation of energy, heat flux *φ*(*x*, *t*)

conservation law in terms of e and *φ*

all as integral

a snag with energy density: temperature [neglected to take board photo]

Objects of two different materials in equilibrium with each other will generally have different energy densities
(think chunks of steel and styrofoam).
This leads us to invent a new measure of thermal energy called *temperature* such that
"temperatures" of objects in equilibrium have the same value.

Got to here, Jan 31, 2017.

Objects of two different materials in equilibrium with each other will generally have different energy densities
(think chunks of steel and styrofoam).
This leads us to invent a new measure of thermal energy called *temperature* such that
"temperatures" of objects in equilibrium have the same value.

volumetric heat capacity

specfic heat capacity

absolute zero

What is the thermal energy content of this brass rod (relative to absolute zero)?

Heat energy flows from hot to cold - let's linearize in the temperature gradient!