Thermal Physics - Flashcards
What is absolute temperature ?
The temperature where the particles have no kinetic energy. Given by the value of 0k
How to convert from kelvin to Celsius ?
K - 273 = degrees Celsius
What is the molecular mass ?
The sum of the masses of all the atoms that make up a single molecule- example h2o
21 +116 = 18
2 hydrogen and one oxygen
What is avogadro’s constant ?
The number of molecules within a mole. (Na)
6.023 * 10 ^ 23
(Carbon 12 isotope - number of atoms within exactly 12 grams of an isotope )
What does 1 mole of a substance mean ?
It is a substance containing Na number of atoms.
What is the equation linking the number of atoms and the number of moles ?
N = n* Na
N - number of molecules or atoms
n - number of moles
What is the molar mass ?
It is the mass of 1 mole of a substance = the molecular mass
Give the relationship between the mass of a substance and the number of moles
Given that M is the mass of 1 mole
The mass of the substance (m) = Mn
Give the relationship between the number of moles and the atoms/ particles in the substance .
Number of atoms in the substance (N) = n*Na
Give the relation between the number of atoms in a substance and the mass of the substance.
N (no of atoms ) = (m/n) * Na = n*Na
What are the conditions/assumptions of ideal gases ?
- gas particles are point masses (same mass + spherical )
- average kinetic energy is directly proportional to the absolute temperature
- particles move in constant random motion
- follow newtons laws
- have a negligible volume compared to the container
- the collisions are elastic
- the motion of the particles are straight
What does Boyles law state ?
At a constant temperature the pressure of a fixed mass of gas is inversely proportional to its volume
What is the equation to find a missing value ( boules law ) ?
P1V1 = p2 v2
As p*v = a constant
What does Charles law state ?
At a constant pressure , the volume of a fixed mass of gas is directly proportional to its absolute temperature
What is the equation to find a missing value ( Charles law ) ?
V1 / t1 =v2 / T2
As v/t is a constant
What does the pressure law state ?
At a constant volume, the pressure p of a fixed mass of gas is directly proportional to its absolute temperature
What is the equation to find a missing value ( pressure law ) ?
P1/ T1 = P2 /T2
As p/t is a constant
At a constant temperature why is there greater pressure when the volume decreases ?
- when the volume is decreased the particles are closer together so collide with each other and the walls more frequently with force producing a greater pressure
Why does the volume increase when the temperature increases at a constant pressure ?
As the temperature increases the particles gain more faster / move further apart taking up a greater volume
What is an isobaric change ?
A change where the pressure is kept constant
How can you change the volume of a gas at a constant pressure ?
Work has to be done ( transferring heat energy ) by heating
What is the equation linking the work done and the pressure and volume ?
Work done = pressure times change in volume
Why does the pressure increase as the temperature increase at a constant volume ?
As the temperature increases the kinetic energy of the particles increase causing them to travel at a faster speed colliding more frequently with a greater force producing a greater pressure
What is the equation you get from combining the three gas laws ?
PV/ T = R ( one mole )
Pv = nRT (n moles )
What is the constant for 1 mole of a (ideal ) gas at room temperature and atmospheric pressure ?
R = 8.31
How can the ideal gas equation be written in terms of the number of molecules in the gas ?
PV = NRT / Na ( n is replaced with N/Na)
Which can be written as PV = NKT
K is Boltzmann’s constant - R/Na
What is Brownian motion ?
The random motion of larger particles in a fluid due to collisions from the surrounding fluid particles. For example pollen grains colliding with water molecules.
What is an example of Brownian motion ?
Smoke particles being pushed around due to the smaller air molecules
What does the Maxwell Boltzmann distribution convey ?
The graph shows that the speeds of the molecules vary in speed ( all are not the same speed )
What does the area under the Maxwell Boltzmann graph give ?
The number of particles
What happens to the maxwell distribution if the temperature increases ?
The peak would shift to the right and would have a greater range producing a lower curve
What is the root mean square speed ? ( crms)
The root of the mean of the speed squares
- initially square the mean then take the mean of them and then root the value
What are the steps to derive the kinetic theory equation ?
- change in momentum:
Particle with mass m with initial velocity u hits the surface and rebounces( elastic collision )
Final momentum - initial momentum
= mu - (-mu ) = 2mu - Time taken = 2l / u
- Rate of change of momentum = change in momentum over time ( mu^2 / l ) can be equated to the force
- force over area = pressure
mu^2 / l^3 (gives us the volume ) - taking multiple speeds of the particles into account :
P= m (u1… squared ) / v
In replace of u1… we sub in (ū ^2 *N ) - taking all directions up and down and sides :
We assume velocity is the same in all directions so ć^2 = 3 ū^2
Therefore aP = 1/3 * Nmć^2 / v
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Steps to derive the the kinetic theory equation :
m is the mass of one particle
N is the number of particles
- change in momentum ( 2mu )
- time taken ( 2l / u )
- rate of change of momentum ( mu^2/ L )
- equate the rate of change of momentum to the force
- divide the force by the area to get the pressure ( mu^2 / l^3 )
- when you look at multiple particles inn the x directions at multiple speeds ( mNū^2 / v
- you then look at multiple directions producing you sū^2 ( 1/3 nmć^2 = PV )
- replace the mean square with crms
PV = 1/3 Nm ( crms) ^2
Define the internal energy of a gas :
- internal energy of a gas is the sum of the randomly distributed kinetic energy and potential energy of all particles in the gas
What is the internal energy of an ideal gas ?
It is just the kinetic energy as ideal gases do not have potential energy due to negligible forces of attraction
