Section 3: Thermal Physics Flashcards
Temperature
The measure of how ‘cold’ or ‘hot’ a substance is
The common property that two bodies possess when they are in thermal equilibrium with each other
A measure of a body’s ability to transfer heat to other bodies
Human blood temp
37°C
98.6°F
Volume and temperature
V ∝ T
When T is below fusion point…
Gas becomes liquid
Triple point of water
A specific combination of pressure and temp at which all three phases of water co-exist simultaneously
Defined as 0.01°C
Celsius and Kelvin
Granularity are same (difference of 1°C is same as difference of 1K)
If problem involves a difference in temp, doesn’t matter if you use °C or K, as long its in the same units
If problem only involves a single temp, must use K
Absolute scale of temperature
Kelvin scale (K)
Using a thermometer
Essentially only gives a reading of its own temp
Thus, it’s critical to wait until the temp of the thermometer becomes the same as the substance you are measuring
i.e. must wait until thermometer is in thermal equilibrium with the substance
Thermal equilibrium
When objects are in thermal contact, their temperatures eventually equalise –> thermal equilibrium
Heat flows from hot to cold objects
Human body - thermal equilibrium?
Human body is NOT at thermal equilibrium with its surroundings
Zero-th law of thermodynamics
If A and B are separately in thermal equilibrium with C, then A and B are in thermal equilibrium with each other
i.e. they are all the same temp
Thermal expansion
Where the size of an object changes with temperature, typically increasing with increasing temp
Length and temperature
L ∝ T
α
Linear expansion coefficient - quantifies change in linear dimensions of an object
Fractional change in length per unit of temp change
Unit K^-1 or °C^-1
β
Volumetric expansion coefficient
Fractional change in volume per unit of temp change
Unit K^-1 or °C^-1
α and β
β = 3α
Solids usually use α (linear)
Liquids and gas usually use β (volume)
Hollows and cavities - heating
Hollows and cavities in solids expand on heating as do the solid parts of the object
Gases - coefficient
All gases have same coefficient, irrespective of their nature
β = 3.4 x 10^-3 K
Solids, liquids and gases - β
Generally:
β(gas)»_space; β(liquid)»_space; β(solid)
Solids: β < 10^-4 K^-1
Liquids: β < 10^-3 K^-1
Gases: β > 10^-3 K-1
Density (ρ) and temperature
ρ ∝ T
Thermal stress
Stress created in objects constrained to a precise, fixed dimension when temp changes occur
Gas
A state of matter where the diff atoms/molecules constituting the material have no bonds betwen them, are v far apart, and are moving around randomly in all directions at high speed
Compressible and deformable
Pressure
The average force (F) per unit of surface area (A)
Pressure - units
Standard unit of pressure is N/m^2 = 1 Pa (pascal)
1 bar = 10^5 Pa
Standard atmospheric pressure
The mean pressure exerted by our atmosphere at mean sea level at the latitude of Paris
1 atm is roughly equal to…
1 bar to within 1%
i.e. 10^5 Pa
Gauge pressure
Refers to pressure measured wrt atmospheric pressure
e.g. if you inflate a tyre to x bar of gauge pressure, that means the absolute (total) pressure inside the tyre is x bar + the current atmospheric pressure (i.e. about 1.5 bar)
1 atm (or 1 bar) pressure = ? of water
Roughly 10m of water
Ideal gas law - points to remember
P is the absolute pressure (not gauge pressure)
T is the absolute temp (in K)
Boltzmann constant
Proportionality constant in gas law, k
Avogadro number
N(A)
Unit is /mol (mol^-1)
Atomic masses
Atomic masses given in periodic table = masses in grams of one mole of that element
Kinetic theory
Describes the behaviour of gases as that obtained by the averaged effect of many microscopic particles (atoms or molecules) moving and colliding rapidly
Volume and pressure
Decreased volume –> increase no of collisions per unit of surface –> increased pressure
Number of particles and pressure
Increased no of particles –> more collisions –> increased pressure
Velocity of particles and pressure
Increased velocity of particles –> stronger collisions –> increased pressure
Kinetic theory - assumptions
Collisions of molecules with other molecules and the container walls are perfectly elastic and of zero time duration
Molecules occupy a negligible volume compared to size of container
Molecules obey Newton’s law of motion (F = ma)
Molecules exert no forces on each other except elastic forces during instantaneous collisions
Average kinetic energy
AKA thermal energy
Shows temp is a measure of the average energy of the particles in the gas
Existence of absolute zero of temp
Can be inferred from average kinetic energy
To lower the temp of a body, one needs to remove energy from its constitutive particles
Since energy is finite, once we have removed all the energy they have, one can’t lower the temp anymore - this is the absolute zero
RMS velocity
The square root of the mean of the square of the velocities of all particles
Molar mass and velocities of particles
Increased molar mass = heavier particles, which are harder to put in motion (have more inertia) –> decreased speed
Distribution of velocities
A graph showing the percentage of particles in a gas having such and such velocity
Bell-shaped curve that depends on temp
Starts from origin and tends towards zero for very large velocities
Tail extends to large velocities for increasing temp
Distribution of velocities - curve max and RMS
Curve maximum (‘most probable’ velocity) is slightly diff that RMS (RMS is slightly lower)
Solid
Can be seen as a collection of bound particles, each of them vibrating due to their averaged kinetic energy
Heating a material - particles
Particles will vibrate more strongly –> increase in average distances –> thermal expansion
Expansion of water
Water density decreases with increasing temp across majority of its liquid range, but does the opp in range of 0 to 4°C
Freezing a cell
Will burst because of the water expanding as it freezes
To determine which phase a substance is, must specify..
Temperature (T)
Pressure (P)
Volume (V)
Phase diagram
Represents which phase a given substance will be found in as a function of T, P and V
Types of phase diagrams (2D)
V-T diagram
P-V diagram
P-T diagram
V-T diagram
P is constant
V varies linearly with T - straight line
Below the bpt, the gas becomes liquid, and as molecules are bound together, volume shrinks significantly - gives discontinuity in V-T curve
Same occurs for liquid to solid, but less obvious
P-V diagram
Hyperbola on right part (vapour phase) of diagrams
Liquid phase curves pretty much verticle
Liquids - compression
Most liquids are largely incompressible - V barely changes when applying pressure because molecules are v close and intermolecular forces resist the applied pressure
P-V diagram - grey zone
Liquid-vapour region
Where liquid and vapour can coexist
Pressure stays constant while volume varies
P-V diagram - critical pressure
The pressure where the co-existence zone of liquid and vapour disappears
This is because the pressure is so large that molecules of a gas would be brought so close tgt that it starts to behave like a liquid
P-V diagram - above the critical point
There is no more distinction between liquid and gas phase
P-T diagram
Volume is constant
Typically contains 3 curves separating the solid, liquid and gas phase
P-T diagram - melting/fusion curve
Line separating solid from liquid
P-T diagram - boiling curve
Line separating liquid from gas
Does not extend indefinitely - it ends at the critical point, above which liquid and gas becomes indistinguishable
P-T diagram - sublimation curve
Line separating solid from gas (lower part)
Sublimation
The process where a solid becomes directly a gas without transition to a liquid
P-T diagram - triple point
Where the 3 curves of the P-T diagram meet
Where all 3 phases coexist
What happens to the molecules that escape the liquid - open container
Infinite space –> escaping molecule will never come back
Evaporation occurs irremediably
THus a liquid can’t stay liquid in a vacuum and is bound to disappear
What happens to the molecules that escape the liquid - closed container
It’s possible for molecules to come back and for evaporation to effectively cease
Called the liquid-vapour equilibrium
Evaporation rate depends on…
Temperature
Evaporation - surface of liquid
Liquid molecules accumulate at surface, resulting in presence of a vapour phase co-existing with the liquid above the surface
Closed container: Condensation rate
Once there is enough molecules in the vapour phase, it may happen that collisions between molecules in the vapour phase may push back some molecules into the liquid
Condensation rate depends on…
Pressure in gas phase
Higher pressure = more molecules = larger the no of suitable collisions
Closed container: Liquid-vapour equilibrium
As more molecules evaporate, the pressure in vapour phase will build up
Condensation rate increases until it’s equal to evaporation rate –> equilibrium is reached
Closed container: Saturated vapour pressure
The pressure in the gas phase where the container is in liquid-vapour equilibrium
How to determine saturated vapour pressure
Can simply be read (for a given temp) on the boiling curve on the P-T diagram
Saturated vapour pressure at a given temp = pressure required to make a liquid boil at that temp
Closed container: Smaller overall volume, but same amount of liquid
Evaporation is unchanged –> same pressure in gas phase required to reach equilibrium
Explains why the curve on the P-V diagram is horizontal in these conditions; pressure is same for diff volumes
Closed container: Larger overall volume, but same amount of liquid
You will reach a point where even when all the molecules are in the gas phase, the pressure will still be too low to overcome the evaporation rate –> substance will be purely in gas phase and have totally evaporated
Closed container: Increased temperature
Evaporation rate increases (more Ek available to kick out molecules in gas phase) –> equilibrium will be reached for a larger pressure (with less liquid and more vapour)
How does boiling occur
Through the presence of impurities or through surface roughness of container
These act as nucleation sites for bubbles of the heated substance to form inside the liquid
Boiling: Saturated vapour pressure
The pressure inside the bubbles in liquid
Boiling: If pressure of surrounding atmosphere (above surface of liquid) is larger than saturated vapour pressure…
The bubbles can’t survive - may rise in lqiuid a bit (through buoyancy forces) but will eventually be crushed by the external pressure
Boiling: As temp rises..
Bubbles grow bigger because of increased evaporation rate
Saturated vapour pressure increases, which eventually becomes = to surrounding atmosphere –> bubbles can withstand crushing pressure of atmosphere –> float and rise to top of liquid –> vapour content leaves liquid at once
The boiling curve also represents…
The saturated vapour pressure
Where does boiling vs evaporation occur
Boiling: bubbles can escape the liquid from anywhere in the volume
Evaporation: molecules can only escape form the surface
Therefore a liquid boils much faster than it evaporates
Dalton’s law
States the total pressure exerted by the mixture is the sum of all the partial pressures
RH = 100%
Liquid and vapour phases are in equilibrium
Atmosphere can’t absorb any more water vapour (if there was, condensation rate would become larger than evaporation rate –> water vapour returns to liquid phase)
We say the air is saturated with water vapour - saturated vapour pressure
Preventing equilibrium in the atmosphere
Currents, winds and inhomogeneities in the atmosphere can prevent equilibrium between the gas and liquid phases of water to be reached locally
Numerator and denominator of RH
Numerator: how much water there is in the air
Denominator: how much space there is for water in the air
Set quantity of water vapour in air, but changing temp - effect on RH
As temp drops, saturated vapour pressure decreases –> RH increases because there is less space for water in the air (saturated vapour pressure is lower)
Dew point
RH = 100%
Depends on partial pressure of water vapour - the more there is, the quicker the dew appears as the temp drops
Determining the dew point for a given level of RH and initial temperature
Use saturated vapour pressure at initial temp and RH to solve for partial pressure of water vapour
Then look at which temp the saturated vapour pressure is = to that partial pressure
This temp = dew point
Heat
The energy transferred from a warm object to a cold object due to their temp difference
Heat vs temperature
Heat is not the same as temp
Temp = energy in an object
Heat = energy in and out an object
What prompts our brains to identify an object as warm or cold
Heat flow - not temperature
Heat units
Joule
Heat symbol
Q
Mechanical and thermal energy
Same thing Mechanical energy (e.g. Ep) can be converted into thermal energy
Calorie
Conversion of calorie to joule is known as the mechanical equivalent of heat
If heat is transferred to an object…
It’s temp increases
When is Q > 0 and Q < 0
Q > 0 when the object temp increases and energy is brought into the object
Q < 0 when the object temp decreases and energy is removed from the object
Specific heat capacity
Coefficient c
Depends on the substance the material is made of and the phase of the substance
Represents how much heat is needed to increase the temp of 1 kg of a substance by 1°C
Water - specific heat capacity
Comparatively large wrt other substances
Molar heat capacity
Coefficient C
Represents the amount of heat needed to increase the temp of 1 mol of substance by 1°C
Thermal inertia and size of object
If one object is much larger than the other, it’s the smallest one that experiences the largest temp change
The larger object essentially acts as a reservoir of constant temp - has larger thermal inertia - harder to change its temp
Latent heat
The transfer of heat due to a phase change
Phase change - temperature
During a phase change, the temp remains constant
e.g. only when all ice has melted (only liquid water left), will the temp rise again
Vapourising water vs melting ice
More energy required to vapourise water than to melt ice
3 diff ways to transfer heat
Convection
Conduction
Radiation
Convection
The physical, macroscopic displacement of matter
Conduction
The physical contact between hot and warm objects, but apart from thermal vibrations, no matter actually changes place
Radiation
The heat transferred by electromagnetic radiation
Heat transport method doesn’t require any matter
Types of convection
Natural/free convection
Forced convection
What type of convection creates convection currents
Natural convection
Conduction vs convection - speed
Conduction is a much slower process than convection - relies on random collisions and a gradual diffuse transfer of energy
Convection - state
If substances in contact are liquid or gas, the temp gradient established will lead to natural convection
When solids are in contact, convection isn’t possible
Conduction: Calculating Q vs Q/t
Q = heat transferred by conduction (in J) Q/t = rate of conductive heat transfer (power, in W)
Thermal conductivity
Constant k in conduction equation
Metals generally have large thermal conductivity
Diffusion
The mass flow due to a difference in conc between diff parts of a fluid
Diffusion: D
Diffusion coefficient
Osmotic pressure
The pressure due to the difference in levels on both sides of the membrane, i.e. the pressure you need to apply on high conc side to maintain the original conc difference
EM radiation/waves
Waves made up of oscillating electric and magnetic fields
How do different types of EM waves differ
By their frequency at which the fields osscilate, or equivalently by their wavelength
Wavelength
The distance between 2 peaks of oscillating fields
Relationship between wavelength and frequency
Inverse
Smaller wavelength = larger frequency
EM waves - energy
When they hit a material, some (or all) or their energy is absorbed –> material heats up
Temperature and EM radiation
Higher temp of object = more Ek its molecules have = vibrate faster = higher f of emitted EM radiation
Emission spectrum
The distribution of the proportion of radiation emitted at each wavelength
Cold vs warm objects
Long wavelength radiation = cold objects (e.g. red)
Short wavelength radiation = hot objects (e.g. blue)
EM radiation - thermal equilibrium
Object absorbs as much EM radiation energy as it emits
Perfect absorber of EM radiation
A body that can absorb all the incoming radiation falling upon it (all wavelengths) with nothing being reflected
Known as a black body
Also the best emitter
Emissivity (e) - values
Blackbody has emissivity of 1 = good emitter
Totally reflecting body (reflects all radiation at all wavelengths) has emissivity of 0 = poor emitter
0 < e < 1 = grey body
What does it mean if mechanical energy is thermalised
Converted into air’s internal energy
Internal energy (U)
The sum of all kinetic energy (and all potential energy) of all particles of the system
First law of thermodynamics
If a system performs some work on the surroundings while consuming some heat, energy conversation imposes that the difference must appear as a change of internal energy
W vs Q when positive
W > 0:
Work is done by the system on the surroundings
Loss of energy for system
Q > 0:
Heat is entering system from surroundings
Gain of energy for system
State variable
e.g. U
Characterises how the system is in its present state without having to know how the system has been put into that state
Transformation ssytem
Changing the state of the system
Heat engine
A device using heat to produce work
Only work if surrounded by 2 thermal reservoirs - a hot one and a cold one
Takes heat (Qin) from hot reservoir, then produces work while releasing some exhaust gas to cold reservoir (Qout)
PV diagram and work
Can find the work produced during transformation using area beneath the PV curve
Isobaric transformation
A transformation where pressure is constant
Curve is horizontal, so area = rectangle
PV diagrams - sign convention
W > 0: transformation goes left to right; machine generates work; it is an engine
W < 0: transformation goes right to left; machine consumes work
Engines work in ____ cycles
Closed
Periodically come back to same original state and repeatedly perform the same transformation
PV diagram - cycle
The SA encircled by the cycle
Isochoric process
A transformation where volume is constant
Curve is a vertical line –> no area –> W = 0
ΔU = Q
What does internal energy depend on
Essentially only depends on temperature
Mono-atomic vs di-atomic gases
Mono-atomic: have 3 degrees of freedom
Di-atomic: have 5 degrees of freedom
where f = degrees of freedom
Isothermal process
Temperature is constant
Slow process
Adiabatic process
No heat exchange is involved
Fast process
Producing work is associated with a temperature ___
Drop
An adiabatic compression is associated with a temperature ____
Increase
Second law of thermodynamics
States it is impossible for irreversible processes to occur
Irreversible processes
Only occur spontaneously in one direction
Thermodynamic temperature scale
Matches with absolute Kelvin scale
Ways to increase efficiency of heat engine
Increase temp difference between hot and cold reservoirs
i.e. increasing hot temp or decreasing cold temp
3rd law of thermodynamics
It’s impossible to lower the temp of any system to the absolute zero of temperature
(because Q(C) can’t be reached as it would amount to a single reservoir engine)
