Question

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 $10^{100}$, whilst a googolplex is $10^{googol}$. Consider the monatomic ideal gas with one mole of particles, room temperature $T = 300$ K, and a volume $V = 22.4$ L (this corresponds to atmospheric pressure). (a) Which of these properties ($S, T, U, \Omega(U)$) are greater than a googol or googolplex, assuming you are using `molecular-level' units (like $k_B$ for $S$, and $k_BT$ for $U$) (b) Which of these are intensive, extensive, or `faster than extensive' (i.e., grows greater-than- linearly with respect to $N$)

          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 $10^{100}$, whilst
a googolplex is $10^{googol}$.
Consider the monatomic ideal gas with one mole of particles, room temperature $T = 300$ K,
and a volume $V = 22.4$ L (this corresponds to atmospheric pressure).
(a) Which of these properties ($S, T, U, \Omega(U)$) are greater than a googol or googolplex, assuming
you are using `molecular-level' units (like $k_B$ for $S$, and $k_BT$ for $U$)
(b) Which of these are intensive, extensive, or `faster than extensive' (i.e., grows greater-than-
linearly with respect to $N$)

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 10^100, whilst
a googolplex is 10^googol.
Consider the monatomic ideal gas with one mole of particles, room temperature T = 300 K,
and a volume V = 22.4 L (this corresponds to atmospheric pressure).
(a) Which of these properties (S, T, U, Ω(U)) are greater than a googol or googolplex, assuming
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)

Added by Francisco R.

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