Ideal Gases Flashcards
What assumptions are made about ideal gases?
- 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
What causes a gas to exert pressure on its container?
Collisions between gas molecules and the container walls.
What does thermodynamics enable us to do?
It lets us make accurate statements about how large physical systems in which we cannot keep track of evolve.
How are heat systems described in terms of macroscopic quantities?
Classical thermodynamics for heat, temperature, entropyβ¦
How are heat systems described in terms of microscopic quantities?
Statistical thermodynamics
What does the zeroth law of thermodynamics state?
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.
Zeroth Law in equation formβ¦
ππ΄ = ππΆ and ππ΅ = ππΆ β ππ΄ = πB
What is the Kelvin scale of temperature?
An absolute scale where a (in T = a(PV/N) + b) was chosen as triple point of water.
If two gases in thermal equilibrium have the same mean translational kinetic energy what can we deduce?
Temperature is directly proportional to PV/Nβ¦
T = a(PV/N) + b
What differs Celsius from Kelvin?
Celsius is not an absolute scale so 0K = 273.15 Celsius.
How does centigrade define temperature?
0 is the freezing point and 100 is the boiling point of water.
What is the ideal gas law (equation)?
PV = nRT
What is the Boltzmann constant in terms of P, V, N and T?
k = PV/NT
What are Boyleβs law, Charlesβ law and Gay-Lussacβs law?
B) PV = constant
C) V β T
G) P β T
What is the pressure of a mixture of ideal gases?
The sum of the partial pressures (using the ideal gas law).
What does the first law of thermodynamics state?
The change in the internal energy of the system equals the heat transfer into the system plus the work done on the system.
βπΈπππ‘ = πππ + πποΏ½
For very small changes how can the second law be written?
dπΈπππ‘ = dπππ + dπποΏ½
What is heat capacity?
The heat transfer Qin required to increase the temperature of a sample by one degree.
πππ = πΆβT
What is specific heat capacity?
Heat capacity per unit mass
c = C/m
What is the molar specific heat?
The specific heat capacity per mole
cβ = C/n
Equation for mean translational KEβ¦
KE = 1/2mv2 = 3/2kT
What does the equipartition theorem state?
When a substance is in equilibrium, there is an average energy of 1/2kT per molecule associated with each degree of freedom
What is a degree of freedom?
A component of position or momentum (including angular versions) that appears as a squared term in the expression for the energy of a system.
How many degrees of freedom does a monatomic ideal gas have?
Three hence the internal energy is given byβ¦
Eint = 3/2NkT = 3/2nRT
What are the expressions for the work done on and by a gas?
Won = -β« P dv
Wby = β« P dv
bounds: Vf and Vi
What are the names for situations with constant V, P or T?
constant V: Isometric, isovolumetric or isochoric
constant P: Isobaric
Constant T: Isothermal
What is the change in internal energy given by for an ideal gas at constant volume?
βπΈπππ‘ = πππ = πΆvβT
or
ππΈπππ‘ = πΆvπT
For the general case of a polyatomic ideal gas at constant volume. What is an expression for heat capacity?
πΆv =1/2ππ per degree of freedom
How many degrees of freedom should a diatomic ideal gas have?
Eight- 3 translational, 3 rotational and 2 vibrational. Hence
Cv = 8/2nR
From experiment how many degrees of freedom does a diatomic ideal gas actually have? Why?
5 because some degrees of freedom do not contribute to the energy.
What is the heat capacity of an ideal gas at constant pressure?
Cp = Cv + nR
or
cβp = cβv + R
What does gamma represent?
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
What is an adiabatic process?
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.
What is a quasi-static process?
A process that happens slowly enough for the system to remain in internal equilibrium.
What equation relates P, V and πΎ?
(ππ/ππ
) π^(πΎβ1) = constant
or
Pv^πΎ = constant
