thermodynamics lecture 1 Flashcards
what is the mechanical equilibrium between two gases?
it is the equality of pressure between two gases on either side of a movable wall
what is the Equation of state?
pV = nRt
What are the 3 laws defining the equation of state and their supporting graphs?
- Boyles law: as pressure increases the volume decreases
- Charles’s law: as pressure increases the temperature increases, and as the volume increases the temperature also increases.
- Avagadro’s Law: as the volume increases the number of moles also increases.
The supporting graphs are on separate notes
what is the molar volume and how can we use the perfect gas law to find it?
the volume occupied by one mole of a chemical compound. It is donated as Vm = V/n
using the real gas equation we can find and expression for V/n = RT/p = Vm
What is the partial pressure?
the partial pressure of a gas a in a mixture of gases is defined as p = xa *p where xa is the mole fraction expressed by Xa = na/ntot (ntot = the total number of moles)
What is Delton’s law?
The pressure applied by a mixture of gases is equal to the sum of the pressures that each gas would exert if it occupied the container alone.
This law is only valid for a mixture of perfect gases.
what is the assumption made in the kinetic theory and the 3 assumptions made in the kinetic model?
in the kinetic theory, it is assumed that the only contribution to the energy of the gas is from the kinetic energy of molecules.
in the kinetic model, it is assumed that:
- the gas consists of mass, m, and is moving in random motion obeying the classical mechanics
- the size of the molecules is negligible, meaning their diameter is smaller than the relative distance between collisions
- the molecules only interact through brief elastic collisions.
What is the mean value equation and its conclusions?
the mean value equation is where we state that the kinetic energy of the gas molecules is equal to their thermal energy giving the following equation:
1/2M<v^2> = 3/2RT
This shows that the speed is proportional to the temperate and inversely proportional to the molar mass of the molecules.
How do you derive an expression for the collision factor using the kinetic model?
Lec notes
what is the relation between repulsion, attraction, and pressure?
Repulsion assits in expansion as repulsive forces are most effective when the molecules are at very very close distances to each other causing high pressures and expansions
attractive forces assist in the compression as the molecules don’t need to be as close to each other causing lower pressure
Note that for attractive forces to work we still need the molecules to be relative to each other.
what is a compression factor?
it is the measured molar volume of a gas to the molar volume of a perfect gas
Z = Vm/V^0m where Z = PVm/RT (since ideal gas equation)
If z>1 repulsive forces are at play
if z = 1 the gas is ideal
if z < 1 attractive forces are at play
What is the virial equation of state?
it is seen that at very large temperatures and high molar volumes, a real gas starts behaving like an ideal gas. This indicated that the ideal gas expression is actually an approximation of a large expansion. The expansion is defined as the virial equation of state:
PVm = RT(1+B/Vm + C/Vm^2 +…..)
B, C are considered Virial coefficients where B/Vm»_space; C/Vm^2»_space; D/Vm^3 indicating that past the second term, the values become extremely small and insignificant
What is Boyle’s temperature?
it is the temperature where the properties of a real gas coincide with the properties of an ideal gas
B’ = 0
PVm = RT(b)
how do we derive the Van der waals equation of state?
Van der waals made an equation that takes into account the repulsive and attractive forces between molecules.
For the repulsive forces, he stated that molecules behave as a small impenetrable sphere rather than moving in a volume V, therefore the corrected volume of the sphere should then be V-nb where nb represents the volume of the molecule itself. This suggests an altered ideal gas equation of P = nRT/(V-nb)
For attractive forces, it is known that the pressure increases with increasing frequency of collisions and increasing force of collisions, which when interactive forces are in play decreases both of these factors overall decreasing the Pressure. The attractive forces increase with the increase in the concentration of the molecules, therefore the pressure would then decrease by the square of the concentration given as a(n/V)^2
After considering both the repulsive and attractive forces the van der waals state equation is stated as
P = nRT/(V-nb) - a(n/V)^2
where a and b are called the van der waals coefficients.
a - represents the strength of attractive interaction
b - represents the repulsive interactions between molecules.
Note that the minimum distance between two sphere is given by 2 radius so V = 4/3 pi (2r)^3
