Thermodynamics 1

Question 1

Centigrade and Farenheit Scale

Answer 1

Tc = 5/9 (Tf - 32)

Question 2

Gas Thermometers

Answer 2

Gas thermometers all agree with each other in the measurement of any temperature as long as the density of the gas is very low.
T = (P/P3)*T3

where
P = observed pressure of gas in the thermometer
P3 = pressure when the thermometer is immersed in a water-ice-vapour bath at its triple point
T3 = 273.15K (the triple point temperature)

Question 3

Ideal Gas

Equation of State

Answer 3

PV = nRT

Question 4

Universal Gas Constant

Answer 4

R = 8.31 J/molK = 0.821 Latm/mol*K

Question 5

Boltzmann’s Constant

Answer 5

k = 1.381x10^-23 J/K

Question 6

Advogadro’s Number

Answer 6

Na = 6.022x10^23

Question 7

Ideal Gas

Equation for a Fixed Amount of Gas

Answer 7

P2V2/T2 = P1V1/T1

Question 8

Kinetic Theory of Gases

Molecular Interpretation of Temperature

Answer 8

The absolute temperature T is a measure of the average molecular translational kinetic energy.

Question 9

Kinetic Theory of Gases

Equipartition Theorem

Answer 9

When a system is in equilibrium, there is an average energy of 1/2 kT per molecule (1/2 RT per mole) associated with each degree of freedom.

Question 10

Kinetic Theory of Gases

Total Translational Kinetic Energy

Answer 10

Ktrans = N(1/2 mv²)av = 3/2 NkT = 3/2 nRT

Question 11

Kinetic Theory of Gases

RMS Speed of Molecules

Answer 11

vrms = √[(v²)av] = √[3kT/m] = √[3RT/M]

Question 12

Kinetic Theory of Gases

Mean Free Path

Answer 12

λ = 1/[√2* nv* d²*π]

nv = number of molecules per unit volume

Question 13

Maxwell-Boltzmann Speed Distribution

Answer 13

f(v) = 4/√π * (m/2kT)^(3/2) * v²*e^[-mv²/2kT]

Question 14

Maxwell-Boltzmann Energy Distribution

Answer 14

f(E) = 2/√π * (1/kT)^(3/2) * E^(1/2)*e^[-E/kT]

Question 15

Calorie and Joule

Answer 15

1cal = 4.184J

Question 16

Heat Capacity

Answer 16

C = Q/ΔT

Question 17

Heat Capacity at Constant Volume and Constant Pressure

Answer 17

Cv = Qv/ΔT
Cp = Qp/ΔT

Question 18

Specific Heat Capacity and Molar Specific Heat

Answer 18

c = C/m
c' = C/n

Question 19

Heat Capacity and Internal Energy

Answer 19

Cv = dEint/dT

Question 20

Heat Capacity for an Ideal Gas

Answer 20

Cp - Cv = nR

Question 21

Heat Capacity at Constant Volume

Monatomic and Diatomic Ideal Gases

Answer 21

monatomic: Cv = 3/2 nR
diatomic: Cv = 5/2 nR

Question 22

Latent Heat of Fusion

Answer 22

Energy required to melt a substance
Qf = mLf

Lf of water = 333.5 kJ/kg

Question 23

Latent Heat of Vaporisation

Answer 23

Energy required to vaporise a liquid
Qv = mLv

Lv of water = 2257 kJ/kg

Question 24

First Law of Thermodynamics

Answer 24

The change in the internal energy of a system equals the energy transferred into the system via heat plus energy transferred into the system via work.
ΔEint = Qin + Won

Question 25

Internal Energy

Answer 25

The internal energy of a system is a property of the state of a system, as are the pressure, volume, and temperature. Heat and work are not properties of state. Eint of an ideal gas depends only on the temperature T. dEint = CvdT

Question 26

Internal Energy of a Monatomic Ideal Gas

Answer 26

Eint = 3/2 nRT

Question 27

Quasi-Static Process

Answer 27

A quasi-static process is one that occurs slowly so that the system moves through series of equilibrium states.

Question 28

Isometric/Isochoric, Isobaric, Isothermal, Adiabatic

Answer 28

``` Isometric/Isochoric = constant volume Isobaric = constant pressure Isothermal = constant temperature Adiabatic = Q=0 ```

Question 29

Adiabatic Process for an Ideal Gas

Answer 29

TV^(γ-1) = constant PV^γ = constant Tγ / P^(γ-1) = constant γ = Cp/Cv

Question 30

Work Done on a Gas

Answer 30

Won = - (Vf,Vi) ∫ PdV

Question 31

Work Done on a Gas | Isometric

Answer 31

``` Vf = Vi Won = 0 ```

Question 32

Work Done on a Gas | Isobaric

Answer 32

Won = - (Vf,Vi) ∫ PdV = -P* (Vf,Vi) ∫ dV = -PΔV

Question 33

Work Done on a Gas | Isothermal

Answer 33

Won = - (Vf,Vi) ∫ PdV = -nRT*(Vf,Vi) ∫ 1/VdV = nRT*ln(Vi/Vf)

Question 34

Work Done on a Gas | Adiabatic

Answer 34

Won = Cv*ΔT

Question 35

Failure of the Equipartition Partition Theorem

Answer 35

The equipartition theorem fails if the thermal energy (~kT) that can be transferred in collisions is smaller than the energy gap ΔE between quantised energy levels. E.g. monatomic gas molecules cannot rotate because the first non-zero energy permitted is much greater than kT.

Question 36

Dulong-Petit Law

Answer 36

The molar specific heat of most solids is 3R. | This is predicted by the equipartition theorem assuming that a solid atom has 6 degrees of freedom.