AQA AL Physics Thermal Physics (SnapRevise)
#physics #Snaprevise Adam Liu
Kinetic Model for States of Matter
- We can explain the properties of solids, liquids, and gases by looking at the structures of the atoms, molecules, and ions that make them up.
- Solids are the most dense state of matter
- The same mass of a substance will normally have a smaller volume than in its liquid or gas forms
- A solid also will not flow
- This is due to the rigid structure of a solid where each particle is held firmly in place and cannot move out of their position.
- Particles in a solid are able to vibrate with some kinetic energy in place but strong intermolecular forces hold them in their structure
- Liquids are generally less dense than solids
- Liquids can also flow
- There is still some restriction on the liquid particle’s motions due to intermolecular forces but is less than that of a solid
- This means that liquids can flow and particles are able to move with a greater kinetic energy than particles in a solid
- Gases are much less dense than liquids
- Gases are also able to flow, although they cannot bee poured in the same way as a liquid
- Gases particles have the most kinetic energy and collide with each other and with the walls of their container
- Particles in a gas are free to move in any direction and have negligible intermolecular forces when they are not colliding with each other.
Internal Energy
- Every Solid, liquid or gas is made up of many molecules
- The kinetic energy is due to the motion of the molecules
- Molecules will also have potential energy due to electrostatic intermolecular forces
- Since it is practically impossible to measure the energies of each individual molecule, we instead treat them as random distributed
- In a system of many molecules such as an object, this assumption will give us accurate predictions
- Instead of worrying about the energies of each of the individual molecules, it is more useful look at the sum of all the energies in a particular solid, liquid, or gas.
- This sum of energies is called the internal energy
- ::The internal energy of an object is the sum of the random distribution of the kinetic and potential energies of its molecules::
Internal Energy of Different States of Matter
- We can illustrate the idea of internal energy by looking at the relative internal energies of solids, liquids and gases
- The molecules in each of these states of matter move in different ways which gives solids, liquids, and gases different internal energies
- In general, we find that the internal energy of a substance is affected more by its molecules’ kinetic energies than potential energies
- Molecules in a gas generally move faster than molecules in a solid or a liquid
- This means that the kinetic energies of gas molecules are generally greater than molecules in liquids or solids
- Hence we expect a gas to have the greatest typical internal energy
- In a solid, molecules cannot move very much as they are fixed in place - they can only vibrate
- They will still have some kinetic energy as they are capable of vibrating in place but it will be much less than that of a gas
- The smaller kinetic energies means that we expect solids to have the smallest typical internal energy
- In a liquid, molecules are not fixed in place like in a solid but do not move as fast as in a gas
- This means that the kinetic energies in a liquid are generally greater than those in a solid and less than those in a gas
- The typical values of the internal energies of liquids are therefore in between those of solids and gases
First Law of Thermodynamics
Increasing Internal Energy by Heat
- The internal energy of a system (such as an object) is the sum of the randomly distributed kinetic and potential energies in all of its molecules
- We can now begin to look at ways of changing the internal energy of a system
- We can do this by changing the kinetic and potential energies of the molecules in the system
- if we add heat to a system, then the kinetic energies of the molecules will increase
- This Weill increase the internal energy of the system
- This is the case for solids, liquids or gases
- Even though molecules in a solid are fixed in a rigid structure, adding heat will still increase their kinetic energies by making them vibrate faster
- We can demonstrate the fact that adding heat increases internal energy by thinking about how we can change states from solid to liquid to gas
- We know that the kinetic energies of molecules in a liquid or a gas are generally greater than that of a solid
- Therefore, if we were to transfer from solid to liquid to gas, we must be increasing the internal energy
- One method of moving from solid to liquid is to add heat to raise the temperature
Increasing Internal Energy by Work
- We can also increase the internal energy of a system by doing work on it
- For example, if you were to compress gas with a piston, the piston would be exerting a force on the gas
- Compressing the gas by exerting a force that moves the piston a known distance means that the piston must be doing work on the gas
- By conservation of energy, this energy from the piston doing work must be converted into some other form
- in fact, the work done by the piston on the gas goes into increasing the internal energy of the gas
First Law of Thermodynamics
- We’ve seen that you can increase the internal energy of a system by adding heat to it or by doing work on it
- This is stated in the First Law of Thermodynamics
- ::The First Law of Thermodynamics states that the change of internal energy of a system is equal to the total energy transfer due to work done and heating::
- This is effectively a statement of conservation of energy
- All this really means is that if we transfer energy to a system by heat or by work, this energy goes into the internal energy
Heat and Thermal Equilibrium
Heat
- From the First Law of Thermodynamics, we have seen that adding heat into a system, such as an object, will raise its internal energy
- This tells us that heat itself is a form of energy in transit
- An object cannot possess heat, but rather heat is the transfer of thermal energy
- For example, if you touch a flame, you will get burned
- The flame transfers thermal energy to your hand
- Similarly, if you place a warm drink inside a cold fridge, the drink will cool down
- The fridge has removed heat from the drink
- These everyday interactions show us that when we put a hot object in contact with a cooler one, heat will transfer from the hot object to the cool one
- These interactions are all transfers of thermal energy
- Note that a transfer of thermal energy always happens at the boundary between the objects or systems of different temperatures
- If you burn your hand on a flame, it is the outer skin and not the inner veins that get burnt first
Thermal Equilibrium
- We have established that heat flows from hot to cold
- If heat flows from hot to cold then we can ask what happens when objects are in contact and are the same temperature
- This state is called thermal equilibrium
- ::Thermal equilibrium is the state in which there is no net flow of Thermal energy between the objects involved; that is, objects in thermal equilibrium must be at the same temperature::
- Note that two objects being at the same temperature doesn’t mean they have the same amount of total thermal energy, only that there is no transfer taking place
- It is useful to note that objects do not have to start in thermal equilibrium to reach thermal equilibrium
- For example, if someone’s hands were cold they could warm them up by holding a warm cup of tea
- The cup of tea transfers heat to their hands
- This heat transfer raises the temperature of their hands and reduces the temperature of the tea
- Eventually, the tea and their hands will have reached the same temperature somewhere in the middle of the two starting temperatures
- At this point, the tea and their hands are in thermal equilibrium and there is no more heat transfer between them
Temperature Scales
Measuring Temperature
- The concept of thermal equilibrium is what allows us to measure temperature
- When we put a thermometer in contact with an object, whichever one of the two stars out hotter will transfer heat to the other
- This transfer of heat goes on until the thermometer is in thermal equilibrium with the object - they are at the same temperature
- The liquid inside the thermometer will expand or contract in a known and predictable way depending on its temperature
- This shows us the temperature of the object that the thermometer is in equilibrium with
- However, we need to match up the level of the liquid in the thermometer to some sort of scale in order to actually measure the temperature
- To do this, we find the measurement on the thermometer at two different known temperatures
- We then divide the area between the two measurements into equal increments
- These increments can then be continued above and below our two chosen reference temperatures to measure temperatures hotter and colder
Temperature in Celsius
- One of the most common temperature scales is the Celsius scale in which temperature is measured in °C
- The two reference temperatures used are the melting point of pure ice and standard atmospheric pressure and the temperature of steam above boiling water
- These reference temperatures are both measured at **standard atmospheric pressure
- The melting point of ice is chosen to be 0°C and the temperature of steam is chosen to be 100°C
- The space in between these on a thermometer is divided into 100 increments of 1°C
- Negative temperatures are simply temperatures below 0°C, the melting point of ice, and temperatures greater than 100°C are simply those greater than the temperature of steam
Problems with Celsius
- Celsius is a useful temperature scale but it does have some downsides
- Firstly, Celsius can have negative temperatures which don’t mean much physically when our chosen point for 0°C is arbitrary (任意)
- Secondly, Celsius uses the melting point of ice and the temperature of steam only at standard atmospheric pressure as reference temperatures
- This is somewhat Arbitrary as standard atmospheric pressure is just the pressure found at sea level on Earth - if we remove ourselves from Earth, there is nothing special about it.
- Even just at the top of a mountain on Earth, the atmospheric pressure is lower so boiling point of water can get as low as 70°C
- If you had to build a thermometer there you would have to recreate standard atmospheric pressure
Temperature in Kelvin
- Another common temperature scale is the absolute scale of temperature which measures temperature in kelvin (K)
- Also known as the Kelvin scale, this scale deals with some of the issues present in the Celsius scale
- Firstly, we get rid of meaningless negative temperatures by putting 0 kelvin (0K) at absolute zero
- Absolute zero is the coldest temperature physically possible so you can never have a negative temperature in kelvin
- Secondly, we deal with the issue of arbitrarily using temperatures at atmospheric pressure by making our second reference point the temperature at the triple point of water
- The triple point of water is a very specific temperature and pressure where water can simultaneously exist as ice, liquid water, and steam
- This only occurs at a temperature of 0.01°C and a pressure of 0.61kPa
- We define the temperature of the triple point, 0.01°C, as being equivalent to 273.16K
- 273.16K is chosen so that the increments of the absolute scale are the same as the increments of the Celsius scale
- This means that an increase of 1°C is also an increase of 1K
- Therefore, as 0.01°C is equivalent to 273.16°C, 0°C must be equivalent to 273.15K
Absolute Zero
Absolute Zero and Internal Energy
- We can show that there must be a minimum possible temperature by considering internal energy
- In particular, we look at the effect of heat on internal energy
- Heating an object will increase the kinetic energies of its molecules, increasing the internal energy
- Temperature is related to internal energy so any change in internal energy will generally come with a change in temperature
- In the same way, removing thermal energy will reduce the kinetic energies of molecules which in turn reduces internal energy and temperature
- A reduction in temperature signals a reduction in the kinetic energies and hence the speeds of molecules
- We can look at the case where all of the molecules are entirely stationary and have zero kinetic energy
- We cannot reduce the speed of a molecule that is entirely stationary so we cannot reduce its kinetic energy
- Reducing temperature reduces the kinetic energies of the molecules so when the molecules are at zero kinetic energy, we are at the lowest possible temperature
- This temperature is defined as 0K or absolute zero
::Absolute zero is the lowest possible temperature, the temperature at which substances have minimum internal energy:: - There is always some potential energy between molecules so this minimum internal energy is never zero
Absolute Zero from Gas Pressure
- We have used internal energy to define absolute zero as the temperature at which none of the molecules have kinetic energy
- We can demonstrate this by changing the temperature of a fixed volume of gas and investigating the effect on the gas pressure
- Gas pressure occurs due to gas molecules colliding with the walls of the container and exerting a force on them
- This tells us that gas pressure cannot drop below 0Pa - this is the pressure at which no collisions happen at all with the walls of the container
- The only time there will be absolutely no collisions between gas molecules and the walls will be when the molecules are entirely still
- We’ve defined absolute zero as the temperature where no molecules have kinetic energy so the temperature we find at 0P must be absolute zero
- In general, we find that if we decrease the temperature of a gas, the pressure also decreases
- If we measure the gas pressure at many different temperatures, we can connect the points with a line
- We can then extend that line backwards until crosses the point where pressure is 0Pa
- We will find that the extended line crosses 0Pa of pressure at a temperature of -273.15°C
- This can be tested for different types of gas and volumes of gas and this point of 0Pa will always be at -273.15°C
- We know that the temperature of a gas at 0Pa is absolute zero so this tells us that absolute zero is at -273.15°C
Introduction to Specific Heat Capacity
Specific Heat Capacity
- To find the change in a particular substances’s temperature during a heat transfer, we have to know its specific heat capacity
::The specific heat capacity of a substance is the Energy needed to raise the temperate of unit mass of substance by 1K::(Miss Alderson version) - We can express specific heat capacity with an equation
- This equation gives us the units of specific heat capacity
- This is more commonly expressed with thermal energy input (Q or E) as the subject
- The sign of energy change there is positive when the object heats up and negative when it cools down
Electrical Method of Finding c
- We can find out the value of specific heat capacity of a material by investigating how the temperature of a known mass of the material changes when we input a known amount of thermal energy
- we can quantify precisely how much thermal energy we are putting into an object by using an electric heater for a known amount of time
- We can use our knowledge of power in a circuit to find exactly how much energy we expect the electric heater to output as heat
- We thermally isolate the material, heater, and thermometer together to ensure that the maximum amount of thermal energy from the heater goes into the material we are investigating
- Once the duration of our experiment has concluded, we find the change in temperature and the amount of electrical energy converted to thermal energy
- Along with the known mass of the sample, we can use this to find the specific heat capacity of the material
Method of Mixtures and Continuous Flow Heating
Method of Mixtures
- We can calculate the specific heat capacity by looking at the temperature at which the two substances reach thermal equilibrium
- Here we assume that as one smaple cools down and other heats up, the only heat transfers are between the two samples and none to the environment
- This assumption allows us to equate the thermal energy gained by the initially cooler sample with the thermal energy lost by the initially hotter sample
Continuous Flow Heating
- So far, we have looked at cases where an object is stationary an is heated or cooled
- A fluid can also flow past a source of heat that raises its temperature as it moves
- This is called continuous flow heating
- For example, water in an electric shower passes through copper coils that are heated by electric heater
- If we have a known flow rate of water in kg s^-1 and a known power, we can divide our equation for temperature change due to thermal energy input by time
- We can replace the thermal energy input per unit time with the power supplied and the mass flowing past the heater per unit time with the flow rate
- We can replace the thermal energy input per unit time with the power supplied and the mass flowing past the heater per unit time with the flow rate
- Here we assume that all of the electrical energy given to the heater goes to heating the water
Change of State
States of Matter
- We know that typical internal energies vary between states of matter
- Gas molecules generally have the most kinetic energy as they are free to move and flow
- This means gases tend to have the most internal energy
- Molecules in a liquid are more restricted in their flow so they have less kinetic energy
- This means liquids tend to have less internal energy than gases
- Molecules in a solid are locked together in strong intermolecular bonds so the kinetic energy in the molecules comes from their vibration
- This vibration involves much less kinetic energy than the flow of gases and liquids so internal energy of a solid is easily the least
Change of State
- Adding heat to a substance can change its state from solid to liquid or liquid to gas
- When this happens, we move from a state with lower internal energy to a state with higher internal energy
- The boiling point of water is 100°C, but if we heat water up to 100°C and turn off the heat, the water will not continue to boil
- The water may still be at 100°C but it will not boil unless heat is continually added to it
- The temperature of boiling water will also not exceed 100°C, even if we keep adding heat
- This shows that a liquid needs to be supplied with extra thermal energy to change state to a gas
- This extra thermal energy only goes into changing state and does not change the temperature
- This input of thermal energy that does not change temperature is needed for a transition from solid to liquid as well
Intermolecular Bonds
- The First Law of Thermodynamics tells us that any input of heat or work must raise the internal energy of a substance
- Adding heat to a substance at a boundary of states of matter must therefore still raise the internal energy
- This added heat will not change the temperature of a substance that is transitioning between states
- Since the temperature is not increasing during a transition between states, the kinetic energies of the molecules is not increasing either
- The internal energy is the sum of the kinetic and potential energies of the molecules so the increase in internal energy must go into increasing potential energies
- These potential energies are due to intermolecular bonds that hold molecules in a solid or a liquid in their structure
The act of breaking these intermolecular bonds requires an input of energy - This energy requirement to break intermolecular bonds is the reason why we have to continuously add heat to boil water at 100°C
- Similarly, the formation of intermolecuar bonds as a substance goes from gas to liquid or liquid to solid will release thermal energy
- This thermal energy released has to be removed from the object in order for it to move from gas to liquid or liquid to solid
Specific Latent Heat
Specific Latent Heat
- We quantify the energy required to change a substance’s state with its specific latent heat
::The specific latent heat of a substance is the energy required per unit mass to change its state without changing its temperature:: - This can be expressed as an equation
- Specific latent heat is different for each substance
Latent Heats of Vaporisation and Fusion
- Specific latent heat takes a differnet value depending on whether the transition is between liquid and gas or between liquid and solid
- When we are looking at transitions between liquid and gas, we use the specific latent heat of vaporisation
::The specific latent heat of vaporisation of a substance is the energy required per unit mass to change its state from a liquid to a vapour without changing its temperature:: - For transitions between solid and liquid, we use the specific latent heat of fusion
::The specific latent heat of fusion of a substance is the energy required per unit mass to change its state from a solid to a liquid without changing its temperature:: - We can use these to express the amount of energy to go from solid to liquid and from liquid to gas with equation
- The specific latent heat of vaporisation is always greater than the specific latent heat of fusion for a substance
- This is because the difference in internal energy between a liquid and a gas is greater than the difference in internal energy between a solid and a liquid
Cooling Effect of Vaporisation
- Specific latent heat of vaporisation helps us explain why sweat has a cooling effect
- When there is sweat on a person’s forehead, it will evaporate even if it is not at water’s boiling point of 100°C
- Water does not necessarily have to be boiling to change into water vapour
- When wet clothes are hung to dry, the water does not boil off the clothes but it still evaporates over time
- The water evaporates because some of the molecules will have a high enough energy to leave the liquid and turn into a gas even at this lower temperature
- The sweat needs an input of thermal energy to evaporate according to the specific latent heat of vaporisation
- This thermal energy comes from the person’s skin, reducing their skin’s internal energy
- This in turn reduces the person’s skin’s temperature, cooling them down
Temperature - Time Graphs
- We can represent the changes in temperature as heat is applied to an initially solid substance with a temperature - time graph
- For most of the graph, the input of heat increases the temperature
- A plateau(高原,高地 - 图中间的部分) occurs when the substance begins melting - any added heat goes into melting the substance instead of raising the temperature
- In order to find the total energy input into the substance we are studying, we have to consider the energy input during the temperature rises separately from when there is a change of state
- we then add all of the energies together to find the total energy input
( Q = 1 + 2 + 3 ) - We can relate the gradient of the temperature - time graph during a temperature rise to the power supplied and the specific heat capacity
- This allows us to compare the specific heat capacity for two different phases of a substance
- The steeper gradient in the liquid section shows us that the liquid phase has a lower specific heat capacity and so heats up faster with the same power input
Specific Latent Heat and Heat Capacity
Specific Latent Heat and Heat Capacity
- To find the total energy input when an substance is heated, we need to consider changes of state separately from any temperature rises
- We have to treat the points where a change of state is taking place separately from the points where we are increasing the temperature
Sign of Specific Latent Heat
- When considering the energy input to convert ice to water, we use the specific latent heat of fusion of ice
- The name refers to fusion which implies that it applies to freezing as well as melting
- The specific latent heat of fusion has the same value whether the object is freezing or melting - the difference is found in the sign of the energy
- Similarly, the specific latent heat of vaporisation has the same value whether the object is condensing (凝结) or boiling with the difference found in the sign of the energy
- When we add heat to the substance, such as when melting ice or boiling water, the energy takes a positive sign
- When we remove heat from the substance, such as in freezing water or condensing vapour (气), the energy takes a negative sign
Brownian Motion
- It is impossible to follow the motions of every molecule in a gas precisely
- We can make accurate predictions with the assumption that molecules move with random velocities
- We can in fact observe that gas molecules move randomly by directing a beam of light through smoke and observing the motions of the smoke particles
- The particles will appear to move in an erratic manner(不稳定的方式), frequently changing their direction and speed
- This occurs because the smoke particles collide with each other and with air molecules that cannot be seen by this method
- Each collision randomises the direction and speed of the particles involved
- This type of motion is called Brownian motion
::Brownian motion is the random and unpredictable motion of a particle such as a smoke particle caused by molecules of the surrounding substance colliding at random with the particle:: - The observation of Brownian motion provided evidence for the existence of gas molecules as they explained what the smoke particles collided with
Kinetic Theory
Need for Kinetic Theory
- We can model molecules in a gas as particles that undergo collisions with each other
- From classical mechanics, we can make predictions of the behaviour of particles when they collide
- We would expect that conservation of momentum would allow us to accurately model the movement of all molecules in gas as they move and collide
- In fact, there are far too many molecules in gas for this to be remotely practical
- For example, in 1m^3 of air, there are roughly 3x10^22 gas molecules
- To model all of these with classical mechanics alone would take a huge amount of computing power
- Instead, we can derive a model for one or two gas molecules using classical mechanics and use averages to scale this up to the whole gas
Kinetic Theory
- In order to model gases statistically, we need to make a series of assumptions:
- We assume that the gas contains a large number of molecules moving in random directions with random speeds (Brownian motion)
- Each molecule occupies a negligible volume compared to the volume of the container
- Every collision between two molecules or between a molecule and the walls of the container is perfectly elastic
- This means that no kinetic energy is lost during a collision
- The time taken by the collisions is negligible compared to the time that the molecules spend travelling between collisions
- Intermolecular electrostatic attraction between molecules are negligible apart from during collisions
- When we apply all of these assumptions, we call our gas an ideal gas
- Predictions made by kinetic theory are theoretical predictions while much of our knowledge of ideal gas behaviour is empirical(经验) - it comes from experiment
Introduction to the Empirical Gas Laws
Empirical Gas Laws
- Much of our knowledge about the behaviour of gases initially came from experiment rather than theory
- Laws found from experiment rather than from theory are called empirical laws
- The gas laws we will discuss only apply when we are dealing an ideal gas
- An ideal gas is one that obeys the same assumptions we make when formulating a kinetic theory of gases
- These are that the gas molecules have negligible volume , move with random motion, and have elastic collisions with each other and the walls of their container
- We also assume that these collisions randomise the velocities of molecules, collisions happen in negligible time and that intermolecular forces are only present during collisions
- We can alternatively define an ideal gas as one that obeys our empirical gas laws
- Our empirical gas laws all relate three features of a gas, its pressure, its volume, and its temperature
Boyle’s Law
- ::the relation between pressure and volume and **at a constant temperature is called Boyle’s law::
- This can also be expressed as a relation betweern pressure and volume before and after a change where temperature is constant
- A change at constant temperature is called an isothermal change
Investigating Boyle’s Law
- To investigate Boyle’s Law, we can vary volume of gas at constant temperature and look at how the pressure changes
- As we do this, we can plot a graph of pressure against volume
- We see that the graph’s shape matches an inverse relationship where p looks proportional to the inverse of V
- If we plot p against the inverse of V
- We see that this graph gives us a straight line which, when extended back past our measurements, goes through the origin
- Since we have a straight line graph, we can fit a relationship between p and V to the equation of a straight line
- This gives us Boyle’s Law
Charles’s Law
- ::Volume and temperature at constant pressure are related by Charles’s law::
- It is important to note that temperature in Charles’s Law is measured in Kelvin
- One way to remember this is that Celsius would allow us to have a temperature of 0°C so we would have to divide by zero(Impossible))
- It is important to reach 0K, or absolute zero, so we never have this problem when using temperature in Kelvin
- Charles’s law can be written as a relation between volume and temperature before and after a change that keeps pressure constant
- ::A change that keeps pressure constant is called an isobaric change::
Investigating Charles’s Law
- We can investigate Charles’s Law by keeping pressure constant and varying either volume or temperature while measuring the other
- For example, we can take measurements of volume while we vary temperature at a constant pressure and plot these on a graph
- If we connect these points, we find that we have a straight line relationship between temperature and volume
- If this line is extended back, we find that it will cross the origin
- Since we have a straight line graph, we can fit a relationship between V and T to the equation of a straight line
- This gives us Charles’s Law
- ::V/T = Constant::
Work Done during an Isobaric Change
- An isobaric change is one where pressure is kept constant
- When a gas expands, work msut be done by the gas to increase the volume of the container - effectively pushing the walls outward
- ::The work done by the gas during an isobaric change of volume is given by an equation::
The Pressure Law
- ::We can relate temperature and pressure at a constant volume using the pressure law::
- It is important to note that temperature in the pressure law is measured in Kelvin
- We can use the pressure law to compare the pressure and temperature of a gas before and after a change at constant volume
- ::A change at constant volume is called an isochoric change::
Investigating the Pressure Law
- We can investigate the pressure law by keeping volume constant and varying either pressure or temperature while measuring the other
- We can take measurements of pressure while we vary temperature at a constant volume and plot these on a graph
- If we connect these points, we find that we have a straight line relationship between temperature and pressure
- If this line is extended back, we find that it will cross the origin
- Since 0Pa is the lowest possible pressure, this graph shows us that 0K is the lowest possible temperature
- Since we have a straight line graph, we can fit a relationship between p and T to the equation of a straight line
- This gives us the Pressure Law
Avogadro’s Constant and Molar Mass
Moles
Still Updating…