Ideal Gases

Question 1

What assumptions are made about ideal gases?

Answer 1

• The molecules are in random motion obeying Newtonian Mechanics
• The total number of molecules is very large
• The molecules can be treated as point-like
• No forces act on the molecules except during collisions
• Collisions are elastic and instantaneous

Question 2

What causes a gas to exert pressure on its container?

Answer 2

Collisions between gas molecules and the container walls.

Question 3

What does thermodynamics enable us to do?

Answer 3

It lets us make accurate statements about how large physical systems in which we cannot keep track of evolve.

Question 4

How are heat systems described in terms of macroscopic quantities?

Answer 4

Classical thermodynamics for heat, temperature, entropy…

Question 5

How are heat systems described in terms of microscopic quantities?

Answer 5

Statistical thermodynamics

Question 6

What does the zeroth law of thermodynamics state?

Answer 6

If two objects are in thermal equilibrium with a third object, then all three of the objects will be in thermal equilibrium with each other.

Question 7

Zeroth Law in equation form…

Answer 7

𝑇𝐴 = 𝑇𝐶 and 𝑇𝐵 = 𝑇𝐶 ⇒ 𝑇𝐴 = 𝑇B

Question 8

What is the Kelvin scale of temperature?

Answer 8

An absolute scale where a (in T = a(PV/N) + b) was chosen as triple point of water.

Question 9

If two gases in thermal equilibrium have the same mean translational kinetic energy what can we deduce?

Answer 9

Temperature is directly proportional to PV/N…

T = a(PV/N) + b

Question 10

What differs Celsius from Kelvin?

Answer 10

Celsius is not an absolute scale so 0K = 273.15 Celsius.

Question 11

How does centigrade define temperature?

Answer 11

0 is the freezing point and 100 is the boiling point of water.

Question 12

What is the ideal gas law (equation)?

Answer 12

PV = nRT

Question 13

What is the Boltzmann constant in terms of P, V, N and T?

Answer 13

k = PV/NT

Question 14

What are Boyle’s law, Charles’ law and Gay-Lussac’s law?

Answer 14

B) PV = constant
C) V ∝ T
G) P ∝ T

Question 15

What is the pressure of a mixture of ideal gases?

Answer 15

The sum of the partial pressures (using the ideal gas law).

Question 16

What does the first law of thermodynamics state?

Answer 16

The change in the internal energy of the system equals the heat transfer into the system plus the work done on the system.

∆𝐸𝑖𝑛𝑡 = 𝑄𝑖𝑛 + 𝑊𝑜�

Question 17

For very small changes how can the second law be written?

Answer 17

d𝐸𝑖𝑛𝑡 = d𝑄𝑖𝑛 + d𝑊𝑜�

Question 18

What is heat capacity?

Answer 18

The heat transfer Qin required to increase the temperature of a sample by one degree.

𝑄𝑖𝑛 = 𝐶∆T

Question 19

What is specific heat capacity?

Answer 19

Heat capacity per unit mass

c = C/m

Question 20

What is the molar specific heat?

Answer 20

The specific heat capacity per mole

c’ = C/n

Question 21

Equation for mean translational KE…

Answer 21

KE = 1/2mv2 = 3/2kT

Question 22

What does the equipartition theorem state?

Answer 22

When a substance is in equilibrium, there is an average energy of 1/2kT per molecule associated with each degree of freedom

Question 23

What is a degree of freedom?

Answer 23

A component of position or momentum (including angular versions) that appears as a squared term in the expression for the energy of a system.

Question 24

How many degrees of freedom does a monatomic ideal gas have?

Answer 24

Three hence the internal energy is given by…

Eint = 3/2NkT = 3/2nRT

Question 25

What are the expressions for the work done on and by a gas?

Answer 25

Won = -∫ P dv Wby = ∫ P dv bounds: Vf and Vi

Question 26

What are the names for situations with constant V, P or T?

Answer 26

constant V: Isometric, isovolumetric or isochoric constant P: Isobaric Constant T: Isothermal

Question 27

What is the change in internal energy given by for an ideal gas at constant volume?

Answer 27

∆𝐸𝑖𝑛𝑡 = 𝑄𝑖𝑛 = 𝐶v∆T or 𝑑𝐸𝑖𝑛𝑡 = 𝐶v𝑑T

Question 28

For the general case of a polyatomic ideal gas at constant volume. What is an expression for heat capacity?

Answer 28

𝐶v =1/2𝑛𝑅 per degree of freedom

Question 29

How many degrees of freedom should a diatomic ideal gas have?

Answer 29

Eight- 3 translational, 3 rotational and 2 vibrational. Hence Cv = 8/2nR

Question 30

From experiment how many degrees of freedom does a diatomic ideal gas actually have? Why?

Answer 30

5 because some degrees of freedom do not contribute to the energy.

Question 31

What is the heat capacity of an ideal gas at constant pressure?

Answer 31

Cp = Cv + nR or c'p = c'v + R

Question 32

What does gamma represent?

Answer 32

The ratio of heat capacities at constant pressure and volume (Cp/Cv). For monatomic gases Cv = 3/2nR and Cp = 5/2nR so gamma = 5/3 and for diatomic gases its 7/5

Question 33

What is an adiabatic process?

Answer 33

One in which there is no heat transfer into or out of a system. They either are very quick or require a well insulated system.

Question 34

What is a quasi-static process?

Answer 34

A process that happens slowly enough for the system to remain in internal equilibrium.

Question 35

What equation relates P, V and 𝛾?

Answer 35

(𝑃𝑉/𝑛𝑅) 𝑉^(𝛾−1) = constant or Pv^𝛾 = constant