1
Q
What is the internal energy,u?
A
- It is the sum of the randomly distributed kinetic and potential energies of the particles in a body
- U= sum of(kinetic energies) + sum of(potential energies)
2
Q
What are the two types of energy that the water particles have in a glass of water?
A
- Kinetic Energy associated with their movement (the faster they move, or vibrate or rotate the higher their kinetic energy (depend on temperature)
- Potential Energy, associated with any forces of interactions between the particles (such as electrostatic attraction or repulsion) (depend on intermolecular forces between the particles)
- IDEAL GASES, in which there are NO intermolecular forces, the internal energy is dependent on ONLY the kinetic energies
3
Q
What is the first law of thermodynamics?
A
- The increase in internal energy of a system is equal to the energy added to the system minus the work done by the system
- Change in U = Change in Q (thermal energy added to system) - Change in W (work done by the system)
4
Q
What is meant by the work done by an expanding gas?
A
When a gas expands it exerts a FORCE on the surrounding, causing them to move: the gas does work on the surrounding
5
Q
How would you determine the work done by an expanding gas?
A
- Expand a gas at constant at a constant temperature (an isothermal change) (consider a gas enclosed in a cylinder by a frictionless piston)
- The gas of volume V experts a pressure, P on the walls of the cylinder
- This in turn exerts a force, F on the frictionless piston of area A so that
- F=pa - This causes an increase in the volume, Change in V, we assume that V is very small and that the force moved the piston at a slow but steady rate such that the external from exerted on the piston, is equal to the force exerted by the pressure, p of the gas in the cylinder
- This effectively makes the pressure exerted by the gas a constant during the expansion
- The gas does work, and so change in W is positive
- The force on the piston moves it through a distance, Change in X such that:
-Change in W = -FChangeinX
= pAchange inX
= pchangeinV
6
Q
What happens when a substance is heated?
A
- The thermal energy is supplied to the particles of the substance, increasing their U and therefore the average kinetic energy of the particles
- This increase in average kinetic energy of the particles, means that there are more frequent collisions so the temperature of the particles rise
- The heat energy increases both the kinetic and potential energy of the constituent particles inside the object
7
Q
What does the size of the temperature change depend on?
A
- The amount of thermal heat energy supplied T (K)
- The mass of the substance, m (Kg)
- The specific heat capacity, c, which is unique to each substance and its state JKg-K-1
- Q=mcchangeinT
8
Q
What happens when you mix a hot and cold liquid?
A
- The internal energy transferred from the hot object when it cools down is equal to the thermal energy gained by the cold liquid and its container and the thermal energy lost to its surroundings
- Q=mcchangeinT (Q is the same for both liquids so then make an equation with the liquids in each on either side of the equal sign)
9
Q
How would you measure the specific heat capacity of water using a continuous flow method?
A
- Fluid moves over an electric heater at a constant rate
- It is assumed that the thermal energy transferred form the apparatus to the surroundings is constant
- The experiment is carried out and then the flow rate of the fluid is changed and a second set of readings is taken
- The heat loss can then be eliminated from the calculations
10
Q
What calculations are carried out in a continuous flow method?
A
- A fluid moves through an insulated tube containing an electric heating wire
- The rise in temperature of the fluid is measured by the two electronic thermometer so that the change in temperature = T2-T1
- The mass of the fluid that flows through the apparatuses in a time t1 is m1 and is measured using a beaker on a balance and a stopwatch
- The flow rate of the fluid is then altered to give another value m2, and the heater controls are change to give the same temperature difference
- The specific heat capacity can then be determined by assuming that the thermal loses to the surroundings are constant for both flow rates
11
Q
How would you figure out the first flow rate in time t1?
A
I1V1t1 = m1cchangeinT + Elost, where I and V are the initial current and pd of the heater and the Elost is the thermal energy lost to the surroundings
12
Q
How would you figure out the second flow rate in time t2?
A
I2V2t2 = m2cchangeinT + Elost
13
Q
Using the two flow rate equations how would you determine the specific heat capacity of the water?
A
-Elost can be assumed to be the same in each experiment so substring the second equation from the first gives:
I1V1t1-I2V2t2 = m1cchangeinT - m2cchangeinT
= cchangeinT(m1-m2)
c = (I1V1-I2V2)t / (m1-m2) change in T
-(if the experiment are both run for the same time t)
14
Q
What happens when a substance changes state? Why is the line steeper at some points?
A
- When a liquid turns into a gas, at the boiling point the temperature change stops as all the thermal energy input is used to overcome the intermolecular forces between the particles of the liquid, converting it into a gas
- It is less steep from solid to liquid as more bonds need to be broken
- Under a phase transition, the temperature remains constant as the kinetic energy does not change instead the effect of heating/cooling is to change the potential energies - Its internal energy changes but its kinetic energy (and temperature) stays the same, and this is because the potential energy off the particles is altered
- For example as a liquid turns into a gas its potential energy increases even though the water molecules in both states are at 100 degrees
15
Q
How do you calculate the amount of thermal energy required to change the state of a substance, without a change in temperature?
A
- Q(J) = m(kg) x l (JKG-1 specific latent heat)
- lv is the latent heat of vaporisation, which is liquid to gas for water
- lf is the latent heat of fusion, which is liquid to solid for water
16
Q
What is the specific latent that of a material?
A
The amount of thermal energy require to change the state of 1kg of material without a change in temperature at a specified ambient pressure (usually 1atm)
17
Q
What is kinetic energy?
A
The energy possessed by a body by its virtue of its relative motion
18
Q
What is potential energy?
A
The energy possessed by an object by virtue of their relative position
19
Q
What is energy?
A
Energy is the capacity to do work
20
Q
What is the heat capacity?
A
- If the heat supplied changeinQ raised the temperature by changing then the heat capacity is:
c=changeinQ / changeinT
21
Q
What is the specific heat capacity?
A
- The heat capacity per unit mass (specific means per unit mass)
c= changeinQ / mchangeinT
22
Q
What is Boyle’s Law? Why?
A
p1V1 = p2V2, when the volume decreases, there are the same amount of particles but in a smaller volume and pace and they are moving at approximately the same speed so there would be more frequent collisions, increasing the pressure
-For a fixed mass of an ideal gas at constant temperature, the pressure of the gas is inversely proportional to its volume
23
Q
What is the pressure law? Why?
A
p1 / T1 = P2 / T2, As the temperature increases, the average kinetic energy of the particles increases so there are more frequent collisions and each collision is faster and harder and so the pressure increases
-The pressure of a fixed mass and fixed volume of a gas is directly proportional to the absolute temperature of the gas
24
Q
What is Charles’ law? Why?
A
V1 / T1 = V2 / T2, as the temperature increases, the average kinetic energy of the particles increases so (there are more frequent collisions and) the particles move about more and so are further apart and so occupy a great volume
-At constant pressure the volume of a fixed mass of an ideal gas is directly proportional to its absolute temperature
25
How do the gas equations combine?
p1V1 / T1 = p2V2 /T2 (pa, mcubed, K)
26
What is absolute zero?
The temperature when all the molecular motion ceases and the pressure of a gas drops to zero. The accepted value is the zero of the Kelvin temperature scale and is defined as -273.15 degrees Celsius
27
What is STP?
- Standard temperature and pressure
| - This refers to 0 degrees (273.15K) and 1.01 x 10tothe5 pa (1atm)
28
What is RTP?
- Room temperature and pressure
| - This refers to 25 degrees (278.15K) and 1.01 x 10tothe5 Pa (1atm)
29
How is pressure and temperature proportional to kinetic energy?
1. p=F/A and temperature is proportional to the average kinetic energy of the constituent particles
2. 3/2KBT = 1/2mvsqaured
30
How do you calculate the pressure with a sphere?
1. Consider a sphere of radius r and a single particle of mass m, travelling with speed v (draw diagram)
2. Assume elastic and frictionless container
3. Find the acceleration of the particle, acceleration is the rate of change of velocity, a vector so need direction and magnitude
- a= v-u / t = vf -vi / t
4. Find radial and tangental vector direction
-Radially: vf - vi = vcostheta - (-vcostheta) = 2vcostheta
-Tangental: vf - vi = vsintheta - vsintheta = 0
-Therefore cannot accelerate in tangental direction so average acceleration MUST be only in radial direction
5. Find t
-Time = d / v = 2rcostheta / v
5. Find Acceleration
- a = vf - vi / t = 2vcostheta / 2rcostheta / v = vsquared / r RADIALLY INWARDS
6. Applying N2 inwards
- F=ma = m x vsquared /r
7. Applying N3 inwards: the force radially outwards on the sphere is F = mvsquared / r
8. Applying the definition of pressure
- p = F/A = mvsquare / r /4pirsquared = mvsqaured / 4pircubed
- p = mvsquared / 4/3pircubed x 3 = 1/3 x 1/V x mvsquared
-pv = 1/3mvsquared
9. Multiply 3/2KB etc by 2/3:
KBT - 1/3mvsquared
10. Therefore pV = KBT and pV / T is a constant as promised (limitations of only one particle)
31
How would you do it for n particles?
6. Fi=mvisqaured / r
1. F = sum of Fi = m/r Sumvisquared = Sum mvisquared/r
2. vbarsquared = Sumvisqaured / n
3. F= m/r Nvsqaured
4. p = F/A = m/r Nvsquared / 4/3 pi r cubed x 3 = 1/3 Nmvbarsquared / v = 1/3 rho vbarsquared
5. pV = 1/3 Nm Vbarsquared = 3/2 x 1/3mvbarsquared x 2/3N = 1/2mvbarsqaured x 2/3 N = 3/2NKBT x 2/3
6. Therefore pV = NKBT
32
How do you get to the ideal gas equation?
1. R = KB x NA
2. N/Na = n
3. pV = N/Na (NAKB) x T = nRT
33
What are the conditions for the ideal gas equation in a box?
1. The gas has volume V, density rho and enclosed inside a cubic box of side L
2. Inside the box there are N identical particles with the same mass, m and the gas particle range of different velocities, c1, c2, c3..cN
3. It is assumed that the volume of the particles is negligible compared to the volume of the box
34
What happens when the particle collided with the shaded region?
1. Consider one particle moving parallel to the x axis, with a velocity c1
2. The particle collides with the shaded region in the diagram
3. The ideal gas theory assumes that the collision is totally elastic and os the particle rebounds back off the wall with a velocity of -c1
4. The particle therefore experience a total change in momentum equal to 2mc1, during the collision
5. If the totally elastic collision assumption was untrue then the particles would gradually lose energy during the collisions and the average velocity of the particles in the box would decrease resulting in a drop in overall gas pressure, and experimental evidence tells us that this does not happen
35
What happens to the particle once it has collided with the side of the box?
1. The particle then travels back across the box, collides with the opposite face, before returning to the shaded wall in a time interval deltat = 2L / c1
2. This means that in the time interval deltat, the particle makes one collision with the wall and exerts a force om it. if the particle obey N2 then:
- F = change in momentum / time = 2mc1 / 2L/c1 = mc1sqaured / L
3. The shaded wall has an area A=Lsqaured, so the pressure exerted by the one particle is:
- p = F/A = mc1squared / L / Lsqaured = mc1sqaured / Lcubed
36
How do you do it with N particle with the ideal gas in a box?
1. There are N particles in the Vox, and if they are all travelling parallel to the x axis: total pressure on the shaded wall would be:
- m/Lcubed x (c1squared+c2squared+c3squared...cNsquared)
2. But in reality the particles are moving in random directions with velocity c, comprising components at right angles to each other in the x, y and z directions (cx, cy, cz). Using 3D Pythagoras csquared = cxsquared + cysquared + czsquared but as on average cxsquared = cysquared = czsquared so cxsquared = 1/3csquared
3. As there are N particles in the box, the pressure p, parallel to the x axis is therefore 1/3 x (above in 1)
4. We now define a quantity called the root mean square velocity (crms) (state what) and so substituting : cubed for V,
pV = 1/3 Nm (crms) squared
5. Nm is the total mass of the gas inside the box, so the density of the gas inside the box is given by
rho = Nm / v so p=1/3 x rho x (crms)squared
37
How is V and n related?
1. In this law he suggested that equal volumes of gases at the same temperature and pressure contained the same number of molecules:
- V1 / n1 = V2 / n2 where n is the number of moles fo the gas
38
What is the Avogadro constant?
Na, is used to reprint the number of particles present in mole of a substance 6.02 x 1023
39
What is the Boltzmann constant?
- KB = R /Na = 1.38 x10-23
- Links the macroscopic measurements of pressure volume and temperature to the microscopic particles in a gas and has a fundamental portion. in the model of an ideal gas
40
How are N, Na and n related?
1. N = Na x n and N is the number of particles in the gas
2. R = NaK, pv = nNaKT, pv=NKT (this implies that the pressure of na ideal gas is independent of the mass of the particles)
41
How are m, Mm and Na related?
1. The molecular mass, m is the mass of one molecule of a substance, the molar mass, Mm is the mass of one mole (Na) of molecules of the substance
2. Mm = Nam
3. If the mass of a known gas is measure, Mg, then dividing this value by the molar mass given the number of moles, n and dividing it by the molecular mass m gives the number of molecules N
- n = Mg / Mm, N=Mg / m
4. Both of these can be substituted into the ideal gas equation, allowing all quantities to be measured macroscopically
- pV = Mg/Mm RT, pv= Mg/mKT
42
What are some of the assumptions of the ideal gas model?
1. An ideal gas consists of a large number of identical small hard spherical molecules
2. All the collisions between the molecules themselves and the contain are elastic and all motion is frictionless
3. The movement of the molecules obey Newton's laws of motion
4. The volume of the molecules is very much smaller tea the volume of the container (treating everything as a point particle)
5. No attractive or repulsive intermolecular forces apart from those that occur during their collisions
6. The time spent during collisions is very much smaller than between collisions
43
How does an ideal gas move?
1. An ideal gas moves in random directions
2. This is important because if this was not true then gases would exert more pressure on one surface of their container than they would on another (the direction that the particles travel in would be important and the theories would be different in different directions
3. The fact that the gases (and all fluid particles) have random molecular motion first observed by Robert Brown (Brownian motion), pollen grains floating on water, grains moving in random directions:
4. Explained later as a result of the cumulative effect of the water molecules randomly hitting the pollen grains
5. At different times the pollen grains are hit by water molecules more on one side than rho are on the other sides, resulting in a motion in that direction that appears random in nature
44
How can pressure be described in terms of molecular motion?
1. Macroscopic pressure is defined in terms of a force acting over a given area
2. The kinetic theory model of an ideal gas shows us that the force is due to the collisions of the molecules with the walls of the container
3. The molecules are moving in random directions with a mean average velocity
4. The particles heat the walls of the container and rebound off at the same speed (all the collisions are elastic)
5. This produces a change in momentum, and the cumulative effect of all the particles colliding over the total inside surface area of the container per second causes a force per unit area, which exerts a pressure acting in all directions (as the motion is random)
45
How can volume be described in terms of molecular motion?
1. The motion of molecule inside a container is random in direction
2. This means that there is no preferred direction, so the molecules will spread out throughout the container filling its volume
3. Gases take the volume of their container
4. If the dimensions of the container are changed, the motion of the molecules will react to the change and will continue to fill the available volume
5. The behaviour pf real gases is closest to that of an ideal gas at low pressures, well away from their phase boundary where they change into a liquid
46
How can temperature be described in terms of molecular motion?
1. For an ideal gas, because there are no intermolecular forces, increasing the temperature of the gas only increases the kinetic energy of the particles
2. This increases the average velocity of the particles
3. The particles still move in random direction and they fill the container
4. Increasing the temperature for a fixed volume increases the pressure because the particles average speed is higher so therefore the change in momentum during collisions with the walls is greater, and the particles hit the walls more often
5. This leads to higher forces and therefore higher pressures
6. Allowing the pressure to remain constant requires the volume to change
47
What is an experiment to investigate Boyle's law?
1. You can investigate the effect of pressure on volume by setting up the experiment shown (diagram)
2. The oil traps a pocket of air in a sealed tube with fixed dimensions
3. A tyre pump is used to increase the pressure on the oil and the Bourdon gauge records the pressure
4. As the pressure increases more oil will be pushed into the tube, the oil level will rise, and the air will compress
5. The volume occupied by air in the tube will reduce
- Measure the volume of air when the system is at atmospheric pressure, then gradually increase the pressure, keeping the temperature constant
- Note down both the pressure and the volume of the air as it changes
- Multiplying these together at any point should give you the same value
- If you plot a graph of p again 1/V you should get a straight line
48
What is an experiment to investigate Charle's law?
1. You can investigate the effect of temperature on volume by setting up the experiment shown (diagram)
2. A capillary tube is sealed at the bottom and contains a drop of concentrated sulphuric acid halfway up the tube - this traps a column of air between the bottom of the tube and the acid drop
3. The beaker is filled with near-boiling water, and the length of the trapped column of air increases
4. As the water cools, the length of the air column decreases
5. Regularly record the temperature of the water and the air in the column length as the water cools
6. Repeat with fresh near-boiling water twice more, letting the tube adjust to the new temperature between each repeat
7. Record the length at the same temperatures each time and take an average of the three results
8. If you plot your average results on a graph of length against temperature and daw a line of best fit, you will get a straight line
9. This shows that the length of air in the column is proportional to the temperature
10. The volume of the column of air is equal to the volume of the cylinder, which is proportional to its length, so the volume is also proportional to the temperature. This agrees with Charle's law
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