Introduction

Question 1

Define Specific value.

Answer 1

Extensive property / Mass.

Question 2

Define Extensive Properties and what example fall into this category.

Answer 2

Variables which scale with the system size.

∝ mass, or a function of mass.

Total KE, (U).

Volume, (V).

Question 3

What questions are permutations used for to answer?

Answer 3

Permutations answer the number of arrangements.

“How many arrangements are there if ……”.

_nP_k = n! / (n-k)! = P(n,k)

Here order does matter, and must be accounted for.

A,B,C ¬= B,A,C …..

Question 4

Define a mole.

Answer 4

A quantity of stuff.

Exactly 6.022 x 10²³ of stuff.

Advogadro’s Number, N_A = 6.022 x 1023 is equivalent to a mole of stuff.

[N_A] = [1/mole].

Question 5

What questions are combintorics used to answer and how do they differ from permutations?

Answer 5

Combintorics are used to answer the number of combinations, as to permutations, but order does not matter and so not be double counted.

_{n<span>C</span>k} = n! / [k! (n-k)!] = C(n,k) = Ω

A,B,C, = B,A,C = C,A,B = ……..

Question 6

Define Intensive Properties and give variables which fall into this category.

Answer 6

Variables which are independent of the scaling of the system’s size.

Not a function of mass.

Pressure, (P).

Temperature, (T).

Question 7

GIve the Ideal Gas Law.

Answer 7

PV = nRT = Nk_BT.

K_B, Boltzmann’s constant = 1.3807 x 10^-23 JK^-1.

n is the number of moles.

R is the ideal gas constant, R = N_A·k_B.

N is the number of molecules, N = n·N_A.

Question 8

The Thermodynamic Limit.

Answer 8

A.K.A. The Macroscopic Limit.

As (# of particles) N→∞, Volume →∞, s.t. (particle density) N/V = constant.

In this limit, macroscopic thermodynamics (classical thermodynamics) is valid. There, thermal fluctuatuions in global quantities are negligible, and all thermodynamics quantities, such as pressure and energy, are simply functions of the thermodyanmic variables, such as temperature and density.

Thus for a macroscopic volume with perhaps the Avogadro number of molecules, fluctuations are negligible, and so thermodynamics works.

Question 9

Why is the ideal gas law considered ideal?

Answer 9

Due to 2 assumptions,

1. No intermolecular forces
2. Molecules are point-like and have zero size.

These expectations are not considered for Real Gases.

Question 10

Define Molar Mass.

Answer 10

The mass of one mole of stuff.

Molar Mass = Mass x N_A, where N_A = 6.022 x 10²³ is equivalent to a mole of stuff.

[Molar Mass] = [kg/mol]

Question 11

Dealing with a mole of atoms can quickly get out of hand when using factorials. One way of bringing large numbers down to size is to look at their logarithms. Thus, if Ω represents the _nC_k then

ln Ω = ?

Answer 11

ln(n!) - ln((n - r)!) - ln(r!).

ln n! ≈ n•ln(n) - n, Stirling’s formula.