3. How large are the numbers of statistical mechanics?
Some of the numbers we use in stat mech will defeat your calculator! A googol is 1011′, whilst a googolplex is 10g.’0. Consider the monatomic ideal gas with one mole of particles, room temperature T = 300 K, and a volume V = 22.4 L (this coresponds to atmospheric pressure). (a) Which of these properties (S, T, U, 12(U)) are greater than a googol or googolplex, assum-ing you are using ‘molecular-level’ units (like kB for S, and kBT for U) (b) Which of these are intensive, extensive, or ‘faster than extensive’ (i.e., grows greater-than-linearly with respect to N)
