Thermal properties of Matter

Question 1

What is the ideal gas law?

Answer 1

pV=nRT
pV=Nk_BT

Question 2

What is an isotherm?

Answer 2

A process for which the n and T are constant
So P is proportional to 1/V for constant n and T

Question 3

When does the ideal gas law work well?

Answer 3

At high temperature and low pressure

Question 4

What is the real gas equation of state?

Answer 4

(P+an^2/V^2)* (V-nb)=nRT
“Van der Waals equation of state”
At high volumes/low densities this is well approximated by the ideal gas law

Question 5

What is STP?

Answer 5

273.15K and 10^5Pa

Question 6

What is the triple point?

Answer 6

The point at which the three phase boundaries meet and all three phases co exist

Question 7

How can we define temperature?

Answer 7

T=T=mv_av^2/(3k_B )

Question 8

What is the kinetic energy?

Answer 8

E_k_av=3/2 k_B T

Question 9

How does pV relate to the velocity?

Answer 9

pV=1/3 Nmv_av^2

Question 10

For the Boltzmann distribution what is v_prob?

Answer 10

Vprob=√(2k_B T/m)

Question 11

For the Boltzmann distribution what is v_rms?

Answer 11

Vrms=√(3k_B T/m)

Question 12

For the Boltzmann distribution what is v_av?

Answer 12

Vav=√(8k_B T/m)

Question 13

What is the energy associated with a given temperature?

Answer 13

k_B T

Question 14

What is k_B T at room temperature (290K)

Answer 14

k_B T=25meV

Question 15

What is the heat capacity of an ideal gas at constant V

Answer 15

C_v=1/n dQ/dT
C_v=1/n dU/dT

Question 16

What is a degree of freedom?

Answer 16

1/2 k_B T=1/2 RT

Question 17

What are the degrees of freedom for translation?

Answer 17

3/2 k_B T=3/2 RT

Question 18

What are the degrees of freedom for rotation?

Answer 18

None for monatomic molecules
For diatomic k_B T= RT as only rotate around y and z axis

Question 19

What are the degrees of freedom for vibration?

Answer 19

k_B T= RT
Does not apply at room temperature

Question 20

What is the mean free path?

Answer 20

We define the mean distance travelled between collisions, “the mean free path” λ
λ=v_rms t_mean=(k_B T)/(4π√2 r^2 P)