Thermal Physics

Question 1

What is the equation for Kelvin?

Answer 1

K = C + 273

Question 2

What is the internal energy of a body?

Answer 2

The sum of the randomly distributed kinetic and potential energies of all its particles.

Question 3

What happens to the particles in a system if it is heated?

Answer 3

The particles gain energy and therefore the average speed of the particles will increase.

Question 4

What is the specific heat capacity of a substance?

Answer 4

The specific heat capacity of a substance is the amount of energy needed to raise the temperature of the substance by 1 K.

Question 5

Name 3 ways in which you can affect the change in temperature of a substance.

Answer 5

The mass of an object, changing the material the object is made from (and so changing the specific heat capacity) or changing the rate of energy transfer (e.g. temperature of heater).

Question 6

What experiment could you use to find the specific heat capacity of something?

Answer 6

You could use a continuous-flow calorimeter.

Question 7

What happens to the internal energy, kinetic energy and temperature during a change of state?

Answer 7

Internal energy changes, kinetic energy and temperature stay the same (e.g. when a liquid turns to a gas, it’s potential energy increases but the temperature stays the same).

Question 8

What is specific latent heat?

Answer 8

The specific latent heat (l) of fusion or vaporisation is the quantity of thermal energy needed to be gained or lost to change the state of 1 kg of a substance.

Question 9

What is Boyle’s law of gas? What is an ideal gas?

Answer 9

At a constant temperature the pressure p and volume V of a gas are inversely proportional. An ideal gas is a theoretical gas that obeys Boyle’s law at all temperatures. pV = constant

Question 10

Describe an experiment which investigates Boyle’s law.

Answer 10

• Oil traps pocket of air in sealed tube
• Use tyre pump to increase pressure on oil
• Use a Bourdon gauge to record pressure. As pressure increases, more oil pushed into tube, oil level rises, air will compress. Volume occupied by air in the tube will reduce.
• Measure volume of air when at atmospheric pressure (πr^2 x length)
• Increase pressure by set interval, keeping temperature constant
• Note down pressure + volume of air - multiplying these at any point should give same value
• Repeat experiment twice more and take a mean for each reading
• Graph of 1/V gives straight line

Question 11

What is Charles’ law of gas? Does an ideal gas obey Charles’ law?

Answer 11

At constant pressure, the volume V of a gas is directly proportional to its absolute temperature T. Yes an ideal gas obeys Charles’ law. V/T = constant

Question 12

Describe an experiment to investigate Charles’ law.

Answer 12

• Capillary tube containing drop of concentrated sulfuric acid positioned halfway up tube. Tube sealed at bottom, so column of air trapped between bottom of tube and acid drop.
• Place tube in beaker of hot water. Position ruler behind tube so can measure length of column of air.
• As water cools, regularly record temperature of water and length of air column.
• Repeat experiment with fresh near-boiling water twice more. Take average of air column for each temperature.
• Should see length decreases as temperature decreases.
• Plot results on graph of length against temperature and draw line of best fit - should be straight line
• V = πr^2l, r^2 remains constant, so length is proportional to volume, therefore it agrees with Charles’ law if it is a straight line.

Question 13

What is the pressure law?

Answer 13

At constant volume, the pressure p of an ideal gas is directly proportional to its absolute temperature T. p/T = constant.

Question 14

What is the Avogadro constant?

Answer 14

The Avogadro constant, NA, defined as the number of atoms in exactly 12g of the carbon isotope Carbon-12. Gives number of atoms in any volume of substance whose mass, in grams, is the same as its relative atomic mass.

Question 15

What is Molar mass? How do you work out the number of molecules in a substance?

Answer 15

Substance containing NA atoms, all of which are identical, is defined as 1 mole of that substance. Molar mass is the mass that 1 mole of the substance would have. Number of molecules in a substance N = nNA where n = the number of moles in a substance.

Question 16

What is the ideal gas equation and how is it formed?

Answer 16

The three gas laws can be combined to derive the ideal gas equation: pV/T = constant. Put in values for 1 mole of ideal gas at room temperature and atmospheric pressure gives the molar gas constant R. Therefore the ideal gas equation is pV = nRT

Question 17

What is the Boltzmann constant?

Answer 17

The Boltzmann constant, k, is equivalent to R/NA - the gas constant for one molecule of gas.

Question 18

How do you derive the ideal gas equation for N molecules?

Answer 18

Combine N = nNA and k = R/NA - Nk = nR

Substitute this into ideal gas equation gives pV = NkT (ideal gas equation for N molecules)

Question 19

What is the equation for work done in changing the volume of a gas? How can you find the energy using a graph?

Answer 19

work done = pΔV

The area under a graph of pressure against volume shows the energy transferred to change the volume of gas.

Question 20

Describe how to derive the pressure of an ideal gas using a cubic box.

Answer 20

• Molecules momentum approaching wall = mu where u is it’s velocity. Assuming collisions are perfectly elastic, when it strikes wall A it rebounds in the opposite direction with -mu : Δmomentum = 2mu
• Time between collisions of molecule and wall A is 2l / u (time = distance/speed) so the number of collisions per second is u / 2l therefore the rate of change of momentum = 2mu x u / 2l
• Force equals the rate of change of momentum so the force exerted on the wall by one molecule is 2mu^2 / 2l which equals mu^2 / l
• This is just for one molecule, so for many molecules with different velocities u1, u2 etc, the total force F of all molecules on wall A is F = m(u1^2 + u2^2 + etc) / l
• Can define a quantity called the mean square speed, as u1^2 + u2^2 + etc / N. Put this is equation before gives F = Nmu2(mean) / l
• Pressure of the gas on wall A is force / area = (Nmu^2(mean) / l) / l^2 = Nmu^2(mean) / l^3 = Nmu^2(mean) / V
• Molecules can move in 3 dimensions, so for general equation you need to include all 3 directions - x, y and z. Calculate speed c using Pythagoras - c^2 = u^2 + v^2 + w^2 where u, v and w are the components of the molecules velocity in x, y and z directions
• Treat all N molecules in same way, mean square speed = u^2(mean) + v^2(mean) + w^2(mean). Since molecules moves randomly, u^2(mean) = v^2(mean) =w^2(mean), so c^2(mean) = 3u^2(mean).
• Substitute into equation for pressure, gives p = Nmu^2(mean) / V — p = 1/3 Nmc^2(mean) / V
• Therefore pV = 1/3 Nmc^2(mean)

Question 21

What is the root mean square speed?

Answer 21

The mean square speed has the units m^2s^-2, so for typical speed you have to square root. The r.m.s speed = √mean square speed. So you can write the pressure equation as pV = 1/3 Nm(crms)^2

Question 22

How can the derivation of the pressure of an ideal gas help explain Charles’ law and the pressure law?

Answer 22

As temperature increases, average speed of molecules increases, so change in momentum increases, so force on walls of container increases.

• If volume if fixed, more collisions and a collision will result in a larger change in momentum so exert larger force on wall
• If pressure remains constant, volume must increase, so time between wall collisions is longer, so rate of change of momentum and the force on the walls is reduced.

Question 23

What are the assumptions in kinetic theory?

Answer 23

-All molecules of the gas are identical
-The gas contains a large number of molecules
-The molecules have negligible volume compared with the volume of the container (i.e. they act as point masses)
-The molecules continually move about randomly
-Newton’s laws apply
-Collisions between molecules are perfectly elastic
-Molecules move in a straight line between collisions
Gas obeying these assumptions is called an ideal gas. Real gases behave like this as long as the pressure isn’t too big and the temperature is reasonably high.

Question 24

How do you derive an equation for the average kinetic energy of gas molecules?

Answer 24

pV = nRT , pV = 1/3 Nm(crms)^2
1/3 Nm(crms)^2 = nRT - multiply by 3/2
1/2m(crms)^2 = 3/2 x nRT / N
Can substitute Nk for nR, where k is the Bolztmann constant, to show that the4 average kinetic energy of a molecule is directly proportional to T - can use 3/2 kT as an approximation for the average kinetic energy of molecules in any substance.
1/2 m(crms)^2 = 3/2 kT
Finally, k = R/NA, so can substitute this is for k, giving
1/2 m(crms)^2 = 3/2 x RT / NA

Question 25

How would you find the total kinetic energy of gas molecules?

Answer 25

Once you find the average kinetic energy, you multiply this by the number of molecules to find the total kinetic energy.

Question 26

What are empirical laws?

Answer 26

Empirical laws are based on observation and evidence - they can predict what will happen but they don’t explain why. For example the gas laws are all based on observations. Whereas kinetic theory is based on theory.

Question 27

How were the gas laws developed over time?

Answer 27

• Robert Boyle discovered the relationship between pressure and volume at constant temperature in 1662 - this is Boyle’s law.
• This was followed by Charles’ law in 1787 when Jacques Charles discovered that the volume of a gas is proportional to temperature at a constant pressure.
• The pressure law was discovered by Guillaume Amontons in 1699, who noticed that at a constant volume, temperature is proportional to pressure.
• 18th century, Boyle’s law explained assuming that gases were made up of tiny particles.
• 1827, Robert Brown discovered Brownian motion

Question 28

How long did it take for people to accept the scientific ideas about gas?

Answer 28

Community only accepts new ideas when they can be independently validated. In the case of kinetic theory, most physicists thought it was a hypothetical model and didn’t exist. Wasn’t until 1900s when Einstein made it widely accepted.

Question 29

What is Brownian motion?

Answer 29

In 1827, Robert Brown noticed pollen grains in water moved with a zigzag, random motion. This type of movement of any particles suspended in a fluid became Brownian motion. Einstein later used Brownian motion to support the kinetic theory model of different states of matter (random motion of pollen grains was a result of collisions with fast, randomly-moving particles in the fluid).