Thermal Flashcards
What is one mole
The number of atoms in 12g of carbon 12
What is molar mass
M
The mass of one mole of substance
Roughly the nucleon number in grams per mole
Mass, moles, molar mass equation
Mass=Moles×Molar Mass
m=n×Mr
What is molecular mass
The mass of one molecule of a substance
Usually very small
How do you work out molecular mass
Molar mass/avocados constant
m=M/Na
Total number of atoms
N=n×Na
Moles×molecules in one mole
Total mass of a substance
Mtotal=n×M (moles×mass of one mole)
Mtotal=n×Na×m (moles×number of molecules in one mole×mass of one mole)
What 4 things is the physical condition or state of a gas describes by
4 state variables
Pressure
Volume
Temperature
Number of moles
SI unit for pressure
Pa
SI unit for Volume
m³
SI unit for temperature
K
SI unit for number of moles
mol
Pressure
The normal force exerted by a gas per unit area/per unit surface area over which the force acts
P=F/A
Volume
Space occupied by a gas, often correlating with the size of a container
Temperature
Measure of average maximum kinetic energy of molecules
A temperature of change of 1°C is a change of how many kelvin
1
Just use a different reference point
Celsius vs Kelvin
Celsius uses the freezing point of water as its zero point (water freezes at 0°C) and defines the billing point of water as 100°C
Kelvin uses absolute zero as its zero point (0K)
A change of 1 is the same for both
What is absolute zero
-273°C
0K
Particles motions associated with heat stop and an ideal gas exerts no pressure
Converting Celsius to kelvin
Tk=Tc+273
Room temperature
20°C
293K
Atmospheric pressure at sea level
101kPa
3 gas laws
Boyle’s
Charles’
Pressure/Gay-Lussac’s
Boyle’s Law
The pressure of a gas is inversely proportional to the volume
At a constant temperature and moles (molecules)
Isothermal
Constant temperature
Boyle’s Law equation
PV=constant
P1V1=P2V2
P1/P2=V2/V1
Explain the graph for Boyle’s Law (P,V)
P=y
V=x
Asymptotes at P=0 and V=0
Inversely promotional graph
Explain the graph for Boyles law (P,1/V)
Directly proportional
Straight line
Through origin
For any given volume, the pressure is higher if the temperature is…
Higher
For any given volume, the pressure is higher if the temperature is…
Higher
Charles’ law
Volume of gas is directly proportional to temperature at a fixed pressure and mass (moles)
Isobaric
Constant pressure
Do you use temperature in kelvin or celcius
Kelvin
Equations for Charles law
V=T×constant
V1/T1=V2/T2
Explain the graph for Charles law (Temp in kelvin)
V=y
T=x
Directly proportional
Straight line
Through origin
Explain the graph for Charles law (temp in celcius)
V=y
T=x
Straight line
Through x axis at -273
Crosses y axis at non zero value
For any given temperature, the volume of gas is higher at a …pressure
Lower
Pressure law
The pressure of a gas is directly proportional to the temperature
At a constant volume
And moles/molecules
Isovolumetric
Constant volume
Equations for the pressure law
P=T×constant
P1/T1=P2/T2
Explain the graph for pressure law (temp in kelvin)
P=y
T=x
Directly proportional
Straight line
Through origin
Explain the graph for pressure law (temp in celcius)
P=y
T=x
Straight line
Crosses x axis at -273
Crosses y axis at non zero value
Equation and ratio for gas law
PV/T=constant
P1V1/T1 = P2V2/T2
In Kelvin
Moles constant
Ideal gas equation
PV=nRT
n=number of moles
R=molar gas constant (formula sheet, 8.31JK-¹mol-¹)
Where does the ideal gas equation come from
PV/T=constant
Since nR are constant, PV/T=nR
So PV=nRT
What is the Boltzmann equation
An alternative form of the ideal gas equation
PV=NkT
How is the Boltzmann equation formed
PV=nRT
n=N/Na
PV=RTN/Na
Boltzmann constant (k=1.38x10-²³JK-¹) = R/Na
So PV=NkT
Why can you obtain another constant for the Boltzmann constant
k=R/Na
Both R and Na are constants
5 assumptions for an ideal gas
Volume of a molecule is negligible compared to the volume occupied by the gas
The intermolecular forces of attraction between the molecules are negligible and only influence eachother during collision
The time between collisions with the container walls and other molecules is much greater than the duration of a collision
The collisions between molecules and collisions with walls of container are elastic
There are a large number of molecules, who’s motion is random
Closest to an ideal gas
Helium
Why is helium closest to an ideal gas
Monatomic so does not form a dipole
Closest to a point mass since a single atom molecule
Interacts weakly with other atoms as it has a full outer shell of electrons
Very low boiling point, 4K
Aside from helium, when do other gases behave more like an ideal gas
High temperatures (far above boiling point) And low pressures (low density so molecules far apart)
When and how was brownian motion first observed
By Robert brown
Noticed the apparent random motion of small pollen parti les suspended in water
Explain brownian motion in terms of the pollen particle
Continously bombarded on all side by water molecules
At any given moment there may be slightly more collisions on one side
Or water molecules hitting the pollen may differ in speeds hence momenta
Giving a resultant force on pollen
So it accelerates in the direction of the resultant force
Because the direction and momentum of collision changes a short time later the resultant force may then be in a different direction
Use the kinetic theory to explain boyles law when the volume of a container decreases
Fixed temperature so momentum change of each molecule the same
Time between collisions decreases
Shorter distance to walls
Increased number of collisions per second
Means total change in moment is greater
Larger force exerted on container walls (F=change in momentum/change in time)
Which means pressure increases since P=F/A
Explain Charles law in terms of the kinetic theory when the temperature of a gas is increased
Average kinetic energy of molecules increases (move faster)
So change of momentum of each collision is greater
To keep the total force and pressure constant the volume increases
Increasing the time between collisions so pressure is constant
Explain the pressure law in terms of the kinetic theory when the temperature of a gas increases
Average kinetic energy of molecules increases (move faster)
So change of momentum of each collision is greater
Volume is constant so the total force increases
Increasing the pressure exerted (P=F/A)
Equation to calculate the speed of particles for kinetic theory and ideal gases
PV=1/3 (Nm(crms)²)
Fusion
Liquid to solid
Vaporisation
Liquid to gas
Condensation
Gas to liquid
Sublimation
Solid to gas
Deposition
Gas to solid
Specific latent heat of fusion
Energy required to change 1kg of substance from a solid into a liquid at its melting point
Specific latent heat of vaporisation
Energy required to change 1kg of substance from a liquid into a gas at its boiling point
Crms
r.m.s
Root mean square of speed
Average of the squares of the speeds of the molecules
Root mean square speed
Speeds of particles are squared
Mean of squares is taken
Square root is taken
Deals with negatives since square before adding
Average kinetic energy of a gas molecule in Joules
1/2m(crms)^2=3nRT/2N=3kT/2=3RT/2Na
Units of crms
m^2s^-2
Mean squared speed/(crms)^2
Speeds of particles are squared and a mean is taken
Quantity is related to the mean kinetic energy of gas molecules
Explain the Maxwell-Boltzmann distribution curve
x=Speed in m/s
y=% of molecules with speed in range +/- 1m/s
As a gas gets hotter the peak (most probable speed) moves to the right and is lower and wider, meaning there are more molecules moving at a high speed and a greater range of speeds
Area stays the same since the number of molecules stays the same
Just fewer moving slowly
Show that the kinetic energy of a gas molecule is proportional to the temperature
PV=1/3Nm(Crms)^2 and PV=NkT
NkT=1/3Nm(Crms)^2 kT=1/3m(Crms)^2 Substitute 1/3 for 2/3 x 1/2 2/3 x 1/2m(Crms)^2=kT 1/2m(Crms)^2=3/2kT
Since Ek=1/2mv^2, Ek=1/2(Crms)^2
Ek=3/2kT
Since 3/2k is a constant, Ek is proportional to T
“Molecules of Helium-4 travel faster than Krypton-84”
Comment on this statement
rms speed is greater for helium than krypton so more (not all) molecules of helium are moving faster
there will still be some molecules of helium moving slower than some of krypton’s due to the Maxwell Boltzmann distribution curve
Heat
The transfer of thermal energy from a substance to its environment
Q
Internal energy
The thermal energy stored within a gas
For real gases this is the sum of the total kinetic and potential energies
For ideal gases this is the total kinetic energy only
Where does the potential energy arise from in a real gas
The electrostatic forces between gas molecules
e.g dipole-dipole or van der waals
Thermal equilibrium
No net energy transfer between them when they are placed in contact
Explain energy transfer if two objects are at different temperatures
Object at a higher temperature will have a greater mean kinetic energy
If the two objects are placed in contact with each other then molecules from each will collide
During the collisions energy will be transferred from the molecules with a higher kinetic energy to the molecules in the lower temperature material with lower kinetic energy
This continues until the mean kinetic energies are equal
At this stage the two objects will have the same temperature and be in thermal equilibrium
Specific heat capacity
The energy needed to raise the temperature of 1kg of a substance by 1K
Why is water used as a coolant
It takes a lot of energy to heat mass of water by 1K than (context of question)
So it removes a large amount of energy as it comes into thermal equilibrium with the object its cooling
Specific heat capacity equation
Q=mc△T
Q in joules
T in kelvin
c in Jkg^-1K^-1
What values are negative when using the specific heat capacity equation for cooling a material
Change in temperature
Energy input, since energy neds to be removed from the system
What materials are best for storing thermal energy
Things like water
With high specific heat capacities
So can store lots of energy with a small increase in temperature
What is calorimetry
The study of energy changes in a system by measuring the heat exchanges with its surroundings
Describe an experiment to measure the heat capacity of the liquid inside the calorimeter
- Measure the mass of the system with and without water using a balance
- Subtract the full from empty to get the mass of water
- Set up a circuit with a voltmeter, ammeter, cell and resistor so the resistor is in the water
- Insulate the beaker with bubble wrap
- Close switch
- Keep current, voltage and mass constant
- Measure and record temperature at regular intervals (e.g every minute) using a thermometer
- Plot a graph of time against change in temperature
- Gradient =
Calculate the specific heat capacity if a p.d of 12V delivers a current of 1.2A for 70s to a sample of material of mass of 0.12kg resulting in a temperature change of 16K
c = Q/m△T
Q = Energy input in Joules = Power x Time (Pt)
P = IV = 1.2x12 = 14.4 Q = Pt = 14.4x70 = 1008
c = 1008/(0.12x16) = 525Jkg^-1K^-1
Changing state equation
Q=ml
Changing temp equation
Q=mc△T
Specific latent heat of vaporisation or fusion equation
Q=ml
Work done, pressure volume equation
W=P△V
Constant pressure
Constant temperature
Constant volume
Isobaric
Isothermal
Isovolumetric
