Thermal

Question 1

Probability of a state

Answer 1

Question 2

Partition β

Answer 2

β = 1 / (kT)

Question 3

Partition function

Answer 3

Question 4

Expectation value of energy (full formula)

Answer 4

Question 5

Expectation value of energy (partition shortcut)

Answer 5

Question 6

Entropy in terms of multiplicity

Answer 6

S = k lnΩ

Question 7

Entropy, given probability of microstates

Answer 7

Question 8

Shortcut entropy expression for monotomic ideal gas

Answer 8

Question 9

Classical limit of the partition function

Answer 9

Question 10

Binomial coefficient

Answer 10

Question 11

Sterling’s formula

Answer 11

Question 12

1st law of thermal

Answer 12

ΔU = Q - W

Question 13

2nd law of thermal

Answer 13

Question 14

Work in a reversible process

Answer 14

δW = P dV

Question 15

Differential form of entropy change of a system undergoing a reversible process

Answer 15

δQ = T dS

Question 16

Integral form of entropy change of a system undergoing a reversible process

Answer 16

Question 17

Fundamental thermodynamic identity

Answer 17

dU = TdS - PdV

Question 18

Temperature given by the fundamental thermodynamic identity

Answer 18

Question 19

Pressure given the fundamental thermodynamic identity

Answer 19

Question 20

Energy Maxwell relation

Answer 20

Question 21

Heat capacity at constant volume

Answer 21

Question 22

Heat capacity at constant pressure

Answer 22

Question 23

Differentiation of the fundamental thermodynamic identity with respect to T

Answer 23

Question 24

Difference of heat capacities of an ideal gas

Answer 24

C_P - C_V = Nk

Question 25

Change in temperature

Answer 25

Q = mcΔT

Question 26

Heat engine efficiency

Answer 26

Question 27

Maximum efficiency of a heat engine

Answer 27

Question 28

Internal energy of a classical ideal gas

Answer 28

Question 29

v_rms

Answer 29

Question 30

Speed of sound in an ideal gas, given pressure and density

Answer 30

Question 31

Speed of sound in an ideal gas, given temperature and mass

Answer 31

Question 32

Fermi-Dirac distribution

Answer 32

Question 33

Bose-Einstein distrubtion

Answer 33

Question 34

Average number of fermions/bosons

Answer 34

Question 35

Approximation of average number of fermions/bosons if energy levels are spaced closely together

Answer 35

Question 36

γ

Answer 36

(f+2) / f

Question 37

Monotomic molecule degrees of freedom

Answer 37

3 translational, f=3

Question 38

Diatomic molecule degrees of freedom

Answer 38

3 translational, 2 rotational, 2 vibrational, f = 5 +2b b=0 at room temperature b=1 at high temperatures

Question 39

Polyatomic molecule degrees of freedom

Answer 39

3 translational, 3 rotational, 2N vibrational, f=6+2N N=number of atoms

Question 40

Solid degrees of freedom

Answer 40

3 vibrational in each kinetic and potential energy f=6