Y2: Thermal Physics Flashcards
What is temperature
A measure of the average kinetic energy of all the particles
What is the unit of the absolute temperature scale
Kelvin (K)
What is absolute zero
The lowest temperature any object could theoretically have, when all the molecules have no kinetic energy
K = 0
°C = -273.15
How do you convert between °C and K
K = °C + 273.15
What is the internal energy of a system
The sum of the randomly distributed kinetic and potential energy of all the particles
- Changed by heating/cooling, doing work on the system (eg. change container shape), etc.
What happens to the average particle speed as temperature increases, and how is this change shown on a graph
Average speed increases (causing Ek to increase).
On a graph of the number of particles against the speed, this causes the curve to flatten out, and spread higher, as the proportion with a higher speed increases.
However, curve still passes through origin, and area under the curve is constant
What is a closed system
A system where no matter is transferred in/out
(Under constant conditions, with constant Internal energy)
What is specific heat capacity
The energy required to increase the temperature of 1kg of a substance by 1K
(Joules)
What is the equation for specific heat capacity
Q = mcΔθ
Q: Change in energy
m: mass
c: Specific heat capacity
Δθ: Change in temperature
How would you calculate the specific heat capacity of a material.
- Measure the mass of a block of the material
- Wrap the block in an insulating material
- Insert a heater and a digital thermometer
- Record the start temp
- Switch on the heater and start a stopwatch
- Record the values of V and I in the circuit (of the heater)
- Record the end temp after a set time
- Calculate E=IVt
- Calculate the specific heat capacity with Q = mcΔθ
How would you calculate the specific heat capacity of a liquid
Using a continuous flow calorimeter:
- The liquid flows continuously over a heater
- Use a thermometer at the start and end to calculate the change in temp.
- Using the time and flow rate, calculate the mass mass of the liquid that is between the thermometers
- Record I and V of the heater to calculate E = IVt
- ∴ Q = mcΔθ + Heat loss
- To cancel out heat loss, repeat the experiment, changing V and the flow rate (mass), so Δθ stays the same
Q1 = (m1)cΔθ + Heat loss
Q2 = (m2)cΔθ + Heat loss
∴ Q2 - Q1 = (m2 - m1)cΔθ
So, c can be calculated
What is specific latent heat
The energy required to change the state of 1kg of a substance without changing the temperature
(Joules)
What is the equation for specific latent heat
Q = ml
Q: Change in energy
m: mass
l: Specific latent heat
How does the internal energy change when the temperature of a substance increases (in 1 state)
As temperature increases, Ek increases, so internal energy increases
How does the internal energy change when a substance changes state (no temperature increase)
Energy supplied breaks the bonds between the particles, increasing the potential energy, so internal energy increases
What is Boyle’s Law
At a constant temperature, pressure and volume are inversely proportional
∴ pV = Constant
How do you investigate Boyle’s Law
- Place some oil in a thin tube with fixed dimensions
- Seal one end and attach a tire pump (with pressure guage) to the other to give a fixed volume of air at atmospheric pressure
- Used a ruler to measure the height of the bubbles of trapped air at different pressures
- Plat a graph of 1/length against pressure
- As V ∝ Length, this will show an inversely proportional relationship between p and V
What is Charles’s Law
At constant pressure, temperature and volume are directly proportional
∴ V/T = Constant
How do you investigate Charles’s Law
- Place a drop of oil half way up a capillary tube
- Seal one end to trap air beneath the drop, but leave the other end open to keep p constant
- Place the tube along side a ruler in a beaker with hot water (assume gas temp = water temp)
- Plot a graph of length against temp as the water cools
- As V ∝ Length, this will show a proportional relationship between T and V
What is the pressure law
At a constant volume, pressure and temperature are directly proportional
∴ P/T = Constant
What is the combined gas law
pV/T = Constant
What happens to the pressure if the temperature of a fixed volume of gas is increases, and why does this change occur.
Increasing the temp increases the Ek of the particles, so the rate of change of momentum of the particles colliding with the wall increases, causing the force acting on the walls to increase.
∴ as P = F/A, P∝F
∴ Pressure increases if V (A) remains constant
What happens to the volume if the temperature of a gas is increases at a constant pressure, and why does this change occur.
Increasing the temp increases the Ek of the particles, so the rate of change of momentum of the particles colliding with the wall increases, causing the force acting on the walls to increase.
∴ as P = F/A, P∝F
∴ For P to remain constant, the SA in which the collisions occur must increase, so the volume is increased.
What are the assumptions about ideal gases in Kinetic theory
- All gas molecules are identical
- The gas contains a large number of molecules
- Molecules have negligible volume compared with the volume of the container (act as point masses)
- Molecules continuously move randomly
- Newtonian mechanics applies
- Molecule-wall collisions are perfectly elastic
- Molecules move in a straight line between collisions (Don’t attract each other)
- The forces during the collision act for much less time than the time between collisions
What is the molecular mass
The sum of the masses of all the atoms that make up a single molecule
(Relative molecular mass = Sum of Relative atomic masses)
What is Avogadro’s constant (NA)
6.02x10^23
The number of atoms in any volume of a substance with a mass in grams the same as it’s relative atomic mass
eg. 12g of C-12
How many molecules are in 1 mole
6.02x10^23
What does Avogadro’s constant show is the same for all gasses at a fixed temperature, volume and pressure.
The number of molecules will be the same for any gas, but the mass will be proportional to the molecular mass
eg. 1g of hydrogen and 16g of oxygen occupy the same volume at the same temp and pressure, and both contain 1 mole.
What is the molar mass of a substance
The mass of 1 mole of a substance, which is the same as the RAM
What is the equation for the number of molecules in a gas
N = nNA
N: number of molecule
n: number of moles
NA: Avogadro’s constant (6.02x10^23)
What is the molar gas constant (R)
8.31 (JK^-1mol^-1)
For 1 mole of gas at room temp and atmospheric pressure
PV/T = 8.31 (JK^-1mol^-1)
What is the ideal gas equation for n moles
pV = nRT
pV/T = R (For 1 mole)
∴ pV/T = nR (For n moles)
∴ pV = nRT
What is Boltzmann’s constant (k)
1.38x10^-23
The value of PV/T (at room temp and atmospheric pressure) for one molecule of gas, so can be calculated from:
k = R/NA
What is the ideal gas equation for N molecules
pV = NkT
N = nNA, ∴ NA = N/n
k = R/NA, ∴ NA = R/k
∴ nR = Nk
pV = nRT
∴ pV = NkT
What is the equation for the work done changing the volume of a gas at a fixed pressure
W = pΔV
What is the Kinetic gas equation
pV = (1/3)Nmc̅^2
A molecule of mass m, with velocity u in a cube of length l
∴ momentum = mu
∴ Rebound perfectly elastic, so momentum = -mu
∴ Δmv = (-mu)-mu = -2mu
Assuming no collisions with other molecules,
speed = distance/t (d=l, s=u)
∴ time between collisions with the same side = 2l/u
Rate of change of momentum = Δmv/t
∴ Δmv/t = (-2mu)/(2l/u)
∴ Δmv/t = (mu^2)/l
Ft = Δmv (impulse)
∴ F = (mu^2)/l
You can calculate the root mean square of the speeds of all the particles:
u̅^2 =(u1^2 + u2^2 + u3^2 +….)/N
∴ F = (Nmu̅^2)/l
p=F/A, and A = l^2
∴ p = (Nmu̅^2)/(l^3)
l^3 = V, ∴ p = (Nmu̅^2)/V
Accounting for the movement of the particles in all 3 directions with Pythagoras: c̅^2 = u̅^2 + v̅^2 + w̅^2
However, movement is the same in all 3 directions.
∴ c̅^2 = 3(u̅^2), ∴ (1/3)c̅^2 = u̅^2
∴ p = ((1/3)Nmc̅^2)/V
∴pV = (1/3)Nmc̅^2
What is the root mean square velocity and how is it calculated
The average of all the square of all the molecules speeds
∴ u̅^2 =(u1^2 + u2^2 + u3^2 +….)/N
What is the equation for the average kinetic energy of a molecule of gas
(1/2)mc̅^2 = (3/2)kT = (3/2)(RT/NA)
pV = nRT, and pV = (1/3)Nmc̅^2
∴ (1/3)Nmc̅^2 = nRT
∴ (1/2)Nmc̅^2 = (3/2)nRT
∴ (1/2)mc̅^2 = (3/2)(nRT/N)
N = nNA, ∴ n/N = 1/NA
∴ (1/2)mc̅^2 = (3/2)(RT/NA)
R/NA = k
∴ (1/2)mc̅^2 = (3/2)kT
What is Brownian motion
Random motion of small particles due to collisions with other fast, randomly moving particles.
- First observed by Robert Brown - 1827
- Einstein showed that this motion supports the kinetic theory model for different states
- Gives evidence that everything is made of atoms
