Atmospheric Thermodynamics Flashcards
When can we use the Ideal Gas Law?
When modelling the atmosphere, not the ocean.
What is the Ideal Gas Law?
p = rho R_a T
Where R_a is the specific gas constant for whichever we are considering.
What is the specific form of the Ideal Gas Law?
pV = R_a T
How do we derive hydrostatic balance?
Consider a column of air at rest with pressure and gravitational forces at equilibrium, cancelling common factor of surface area and letting dz tend to 0 gives the definition of the derivative, dp/dz = -g rho
When can we not apply hydrostatic balance?
In areas of strong convection. Otherwise applicable for areas of constant motion or at rest.
What result can we deduce using hydrostatic balance and assuming density is constant in the ocean?
p’ = p0 - rho0gz’
Hence, pressure increases with depth.
What does the variable e_s denote?
The maximum saturation vapour pressure (the most amount of water the air can hold)
What is the equation that relates the rate of change of e_s t with temperature to latent heat of vaporisation?
de_s/dT = Le_s/(R_w T^2)
How do we calculate relative humidity?
e/e_s x 100 (%)
Physical meaning: proportion of stauration for an atmospheric parcel with water vapour pressure e.
What is a function of state (and give examples)
Temperature, pressure, enthalpy and mass (no other prior knowledge to needed to deduce these values) These variables are able to be differentiated.
What are path-dependent quantities and give examples.
Difficult-to-differentiate values that need prior knowledge to deduce a value from. E.g. how much heat is added to a substance (must know difference in thermal energy)
Which key properties must be used in deriving the differentiable form of delta Q?
Assume we have a closed system, in which the total amount of matter
remains constant. Begin from the differential form of the equation relating heat added, work done and change in internal energy. Assume heat is added, and the plunger stays constant so pressure/temperature must change to compensate, substitute in the ideal gas law.
What is the differential form of the equation relating heat added, work done and change in internal energy.
delta Q - delta W = dU
How do we define enthalpy as a function of state? And how do we differentiate?
H = U + pV, consider dH evaluated at constant volume and then constant pressure (chain rule).
