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Physics A - Level > Further Mechanics and Thermal Physics (4): Gases > Flashcards

Further Mechanics and Thermal Physics (4): Gases Flashcards

1
Q

Definition of the Gas Laws

A

The gas laws describe the experimental relationship between pressure, volume and temperature for a fixed mass of gas

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2
Q

Definition of pressure of a gas?

A

The force per unit area that the gas exerts normally on a surface

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3
Q

What is the equation for pressure?

A

Pressure = F/A

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4
Q

What is the unit of pressure?

A

Pa

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5
Q

State Boyles Law

A

For a fixed mass of gas at constant temperature,

pV = constant

where:
p - gas pressure
V - gas volume

(how pressure changes with volume for a fixed mass of gas at a fixed temperature)

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6
Q

What is the definition of an ideal gas?

A

A gas that obeys Boyle’s Law

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7
Q

What is any change at a constant temperature called?

A

Isothermal change

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8
Q

How do you plot results that show Boyle’s Law?

A

Boyle’s Law states that pV = constant for a gas of constant mass at a constant temperature

  • If you plotted a graph of pressure against volume then your gradient would be = 1/k. Therefore as Volume increased pressure would decrease in an inversely proportional relationship.

However, you want to plot a pressure-1/V graph so then your gradient = k. This means you will get a straight line through the origin assuming the gas follows Boyle’s Law

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9
Q

What happens to the pressure as volume is increased for a gas following Boyle’s Law at increasingly high temperatures?

A

As volume increases the the pressure would decrease but by less as the temperature of different samples of the gas were increased -> this means that the constant, k, would become larger

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10
Q

State Charles’ Law

A

For a fixed mass of gas at a constant pressure,

V/T = constant

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11
Q

How to remember that Boyles Law is for a constant temperature?

A

Boyle -> Boiling -> to do with temperature

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12
Q

What is any change at a constant pressure called?

A

Isobaric change

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13
Q

What is the equation for the work done by the gas on a piston when investigating Charles’ Law in order to keep the pressure constant?

A

Work done = p(delta)V

(delta)V - change in volume of the gas

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14
Q

How do you plot the results that show Charles’ Law?

A

Charles’ Law states that for a gas of constant mass at a constant pressure,

V/T = constant

Plot a graph of V against T (Kelvin) and the graph should be a straight line through 0K

NB - If you plot temperature in celsius then you can extrapolate your data to determine the value of absolute 0

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15
Q

State the pressure Law

A

For a gas of fixed mass as constant volume;

p/T = constant

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16
Q

How do you plot the results that show the pressure law?

A

The pressure Law states that for a gas of fixed mass at a constant volume,

p/T = constant

Plot a graph of p against T (kelvin) and the graph should be a straight line through 0K

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17
Q

What is Brownian Motion?

A

The observed random movement of smoke particles (as they are bombarded unevenly and randomly by individual molecules) when a beam of light is directed through it

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18
Q

Definition of the Avogadro constant, N?

A

The number of atoms in exactly 12g of the carbon-12 isotope

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19
Q

How do you find the mass of an atom of carbon-12?

A

mass = 12/avogadros constant

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20
Q

What is the definition of molar mass?

A

the mass of 1 mole of a substance

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21
Q

What is the unit of molar mass?

A

kgmol^-1

22
Q

State the combination of the 3 experimental gas laws

A

For a fixed mass of gas,
pV/T = constant

23
Q

What is the value of the molar gas constant, R?

A

8.31JK^-1mol^-1

24
Q

All ideal gases of the same volume, pressure and temperature contain the same number of…?

A

Moles

25
Q

At standard conditions pV/T =…?

A

8.31 (gas constant)

26
Q

What is the gradient equal for a graph of pV against T for n moles of an ideal gas?

A

Gradient = nR

27
Q

State the ideal gas equation

A

pV = nRT

28
Q

What is the molecular mass, Ms, of a substance?

A

The molar mass of a substance multiplied by the number of moles, n

29
Q

How do you derive pV = NkT?

A

pV = nRT

n (number of moles) = N/Na

where:
N = number of molecules
Na = avogadros constant

k = R/Na

therefore:
pV = Nkt

k - Boltzmann’s Constant

30
Q

Explain Boyle’s Law

A

The pressure of a gas at a constant temperature is increased by reducing its volume because the gas molecules travel less distance between impacts at the wall. Therefore, there are more impacts per second and so the force exerted over an area per second increas -> pressure increases

31
Q

Explain the pressure law

A

The pressure of a gas at a constant volume is increased by raising its temperature. The average speed of the of the molecules therefore increases and so the impacts on the container walls are HARDER and MORE FREQUENT -> pressure increases

32
Q

Describe the spread of speeds in an ideal gas

A

If you plotted a graph of no. of molecules with speed v against speed v then the distribution would be a continuous spread

-> the graph would be in the shape of a bell curve

33
Q

Does the distribution of the speeds of molecules of an ideal gas change from gas to gas?

A

No

34
Q

Does the individual speed of a molecule change as it collides with another molecule?

A

Yes

35
Q

What is the only factor that will affect the distribution of the speeds of the molecules in an ideal gas?

A

Temperature

36
Q

Equation of root mean squared speed of molecules of an ideal gas

A

c(rms) = { c1^2 + c2^2 + c3^2 … + cN^2 / N }^1/2

Where:
c1, c2, c3 ,cN - represent the speeds of individual molecules
N - the number of molecules in the gas

37
Q

Is the root mean squared speed of molecules of an ideal gas the same as the mead speed of molecules in a gas?

A

NO

Mean speed - Sum of individual speeds/ N number of molecules

38
Q

How does the temperature affect the c(rms) of molecules in an ideal gas and therefore, affect the graph of the distribution of the molecular speeds?

A

If the temperature of the gas is raised then is molecules move faster on average therefore the c(rms) increases.

This means that the distribution curve becomes flatter and broader as at higher temperatures there are more molecules moving at higher speeds (Boltzmann distribution)

39
Q

What is the difference between how the kinetic theory equation was devised compared to the gas laws?

A

Kinetic theory equation - mathematics and theories
Gas Laws - experimentally

40
Q

State the kinetic theory equation

A

pV = 1/3 Nmc(rms)^2

Where:
N - number of identical molecules
m - mass of identical molecules
c(rms) - Root mean square speed of the gas molecules

41
Q

What assumptions have to be made when deriving the kinetic theory equation?

A
  • The molecules are point molecules (the volume of each molecule is negligible compared to the volume of the gas)
  • They do not attract each other -> If they did the effect would be to reduce the force of there impacts on the container walls
  • They move in continual random motion
  • The collision they undergo with each other and with the walls of the container are elastic (no overall loss of KE)
  • Each collision with the surface of the container is much shorter than the time between impacts
42
Q

What is the change in momentum due to the impact with the wall of container for a single molecule of an ideal gas?

A

(delta) momentum = -mux - (mux)
= -2mux

ux - velocity in the x direction

43
Q

What is the time given between successive impacts of a molecule of an ideal gas with the face of a container?

A

t = total distance to opposite face and back/ x component of velocity

= 2lx/ux

44
Q

What is the force on an ideal gas molecule between successive impacts on the same spot of the wall of a container?

A

F = (delta) momentum/ time

= -2mux/ (2lx/ux)

= -m(ux)^2/lx

45
Q

What is the force on a a spot of the wall of a container that has been hit by an ideal gas molecule that has travelled to the opposite wall and back?

A

m(ux)^2/lx

46
Q

What is the definition of the internal energy of an ideal gas?

A

The sum of the random distribution of the kinetic energies of its molecules

47
Q

What is the equation for the mean kinetic energy of a molecule of an ideal gas?

A

1/2 m[c(rms)]^2

OR

3/2 kT

OR

3RT/2Na (as k = R/Na)

48
Q

What is the equation for the total kinetic energy of one mole of an ideal gas?

A

mean kinetic energy equation x NA

e.g

3/2 kT x NA = 3/2RT

49
Q

What is the equation for the total kinetic energy of n moles of an ideal gas?

A

kinetic energy of one mole x n

e.g

3/2 RT x n = 3/2 nRT

50
Q

What is the equation for the total kinetic energy of n moles of an ideal gas at temperature T?

A

3/2 nRT

51
Q

What is the equation for the internal energy of n moles of an ideal gas at temperature T?

A

3/2 nRT

52
Q

For an ideal gas total kinetic energy =…?

A

Internal energy

Physics A - Level (22 decks)

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