EOS for Ideal & van der Waals Gases Flashcards
(22 cards)
What does temperature measure in thermodynamics?
The thermal energy of a system; in equilibrium: 𝐸̄ = (1/2)kᴮT
State the Zeroth Law of Thermodynamics
If A and C are in thermal equilibrium with B, then A and C are in equilibrium with each other.
What is an equation of state?
A mathematical function ϕ(P, V, T, N) = 0 that relates state variables.
How many variables are needed to define a state in a closed 3D system?
Two; the third is obtained via the equation of state.
What are the assumptions of the ideal gas model?
Point particles, elastic collisions, and no intermolecular forces.
Derive pressure for an ideal gas from collisions.
P = (N m vₓ²)/V; relates pressure to kinetic energy density
What is the average kinetic energy of a single ideal gas molecule?
KE = (3/2)kᴮT
How is the ideal gas law derived?
Combining microscopic (P = Nmvₓ²/V) and thermodynamic (KE = 3/2kᴮT) gives PV = nRT
What does rms speed of molecules depend on?
vₘₛ = √(3kᴮT/m) → increases with temperature, decreases with molecular mass.
What is number density and how is it calculated?
ρₙ = N/V = P/(kᴮT)
Why does ideal gas law fail at high pressures/low temperatures?
Molecule volume and intermolecular forces become non-negligible.
Define isothermal, isobaric, and isochoric processes.
Isothermal: T constant
Isobaric: P constant
Isochoric: V constant
What two corrections does van der Waals make to the ideal gas law?
Volume: V → V – nb
Pressure: P → P + a/ν² (ν = molar volume)
State the van der Waals equation.
(P + a/v²) (V - nb) = nRT
What does the ‘a’ parameter account for in the vdW equation?
Attractive forces between particles (reduces pressure).
What does the ‘b’ parameter account for?
Finite volume of gas molecules (reduces available volume).
How is the critical point (CP) found from the vdW EOS?
where dP / dV T = 0 and d²P / dV² T = 0
supposed to be partial derivatives
Ideal Gas Law
PV = nRT
Kinetic energy of molecules
KE = (3/2)kᴮT
RMS speed of molecule
v rms = √3KbT/m
vdW Equation of State
(P + a/v²) (V - nb) = nRT
a = Attractive forces between particles (reduces pressure).
b = Finite volume of gas molecules (reduces available volume).
Force from momentum change
F = change in p / change in t
