Thermal physics Flashcards
Energy transfer between two objects takes place if
one object exerts a force on the other object and makes it move i.e. on object does work on the other; or if energy is transferred by heating because of a temperature difference between two objections (conduction, convection, radiation)
The internal energy of an object is
the energy of its molecules due to their individual movements and positions. The internal energy of an object due to its temperature is sometimes called thermal energy
the sum of the random distribution of the kinetic and potential energies of its molecules
The internal energy of an object is increases because of
energy transfer by heating the object, or work done on the object (e.g. by electricity)
If the internal energy of an object stays constant then either
there is no energy transfer by heating and no work is one or energy transfer by heating and work done balance each other out
First law of thermodynamics
the change of internal energy of the object = the total energy transfer due to work done and heating (when work is done/energy transferred by heating)
A molecule is
the smallest particle of a pure substance that is characteristic of the substance
An atom is
the smallest particle of an element that is characteristic of the element
Structure of solid
In a solid, the atoms and molecules are held to each other by forces due to the electrical charges of the protons and electrons in the atoms. The molecules in a solid vibrate randomly about fixed positions. The higher the temperature of the solid, the more the molecules vibrate. The energy supplied to raise the temperature of a solid increases the kinetic energy of the molecules. If the temperature is raised enough, the solid melts. This happens because its molecules vibrate so much that they break free from each other and the substance loses its shape. The energy supplied to melt a solid raises the potential energy of the molecules because they break free from each other.
Structure of liquid
In a liquid, the molecules move about at random in contact with each other. The forces between the molecules are not strong enough to hold the molecules in fixed positions. The higher the temperature of a liquid, the faster its molecules move. The energy supplied to a liquid to rise its temperature increases h kinetic energy of the liquid molecules. Heating the liquid further causes it to vaporize. The molecules have sufficient kinetic energy to break free and move away from each other to become a gas.
Structure of gas
In a gas or vapour, the molecules also move about randomly but much further apart on average than in a liquid. Heating a gas or a vapour makes the molecules speed up and so gain kinetic energy.
Increasing the internal energy of a substance increases the
kinetic and/or potential energy associated with the random motion and positions of its molecules.
The temperature of an object is
a measure of the degree of hotness of the object. The hotter an object is, the more internal energy it has.
Thermal equilibrium when
two objects are of the same temperature so o overall energy transfer by heating will take place.
A temperature scale is defined in terms of
fixed points which are standard degrees of heat that can be accurately reproduced.
Celsius properties
ice point, 0, temperature of pure melting ice; steam point, 100, temperature of steam at standard atmospheric pressure
The absolute scale of temperature, kelvins properties
absolute zero 0K which is lowest possible temperature, the triple point of water 273K, which is the temperature at which ice, water and water vapour co-exist in thermodynamic equilibrium
Celsius –> Kelvins
+273.15
An object at absolute zero has
minimum internal energy as no object can have a lower temperature
Graph of gas pressure against temperature
Crosses y-axis at 0C or 273K and cuts x axis at -273C or 0K for any volume or type of gas
The specific heat capacity, c, of a substance is
the energy needed to raise the temperature of uni mass of the substance by 1K without change of state.
Unit of specific heat capacity
Unit J/kgK
To raise the temperature of mass m of a substance from temperature a to temeperature b
Q=mc(b-a)
Continuous flow heating
in an electric shower, water passes steaily through copper coils heated by an electrical heater. The water is hotter at the outlet than at the inlet. The electric energy supplied per second IV = mc(b-a)/t so for a solar heating panel, the energy gained per second by heating the liquid that flows through the panel is equal to mc(b-a)/t
The density of a gas is much less than the density of the same substance in the liquid or the solid state. This is because
the molecules of a liquid and of a solid are packed together in contact with each other. In contrast, the molecules of a gas are on average separated from each other by relatively large distances.
Liquids and gases can flow, but solids cannot. This is because
the atoms in a solid are locked together by strong force bonds, which the atoms are unable to break free from. In a liquid or gas, the molecules are not locked together. This is because they have too much kinetic energy, and the force bonds are not strong enough to keep the molecules fixed to each other.
When a solid is heated at its melting point
its atoms vibrate so much that they break free from each other. The solid therefore becomes a liquid due to energy being supplied at the melting point. The energy needed to melt a solid at its melting point is called latent heat of fusion
Latent heat is released when
a vapour condenses. This happens because the vapour molecules slow down s the vapour is cooled. The molecules move slowly enough for the force bonds to pull the molecules together to form a liquid.
Sublimation
when a solid vaporises directly when heated
More energy is needed to _____ a substance than to ____ IT
More energy is needed to vaporise a substance than to melt it
The specific latent heat of fusion of a substance is
the energy needed to change the state of unit mass of the substance from solid to liquid without change of temperature
The specific latent heat of vaporisation of a substance is
the energy needed to change the state of unit mass of the substance from liquid to vapour without change of temperature
Q=ml
(l is the specific latent heat with unit J/kg)
Energy transferred when its state changes
Q=ml
Energy transferred when its temperature changes
Q=mc(b-a)
Temperature time graph for a solid being heated
y=x for solid, then melting point, then y=c, then y=x for liquid, then boiling point, then y=x for gas
If the solid has a large specific heat capacity than the liquid, the rate of temperature rise of the solid is
less than that of the liquid
For a pure substance, the change of state is
at constant temperature
Pressure =
force per unit area that the gas exerts normally on a surface
Pressure is measured in
pascals, where 1 Pa = 1Nm^-2
The pressure of a gas depends on
its temperature, the volume of the gas container, and the mass of gas in the container
Boyle’s law states that
for a fixed mass of gas at constant temperature, pV = constant
Graph of pressure (y) against 1/volume
y=mx
Graph of pressure against volume is
a parabola that tends towards each axis. A higher temperature shifts the curve outwards
A gas at very high pressure does not
obey Boyle’s law. The molecules are so close to each other than the molecules’ own volume becomes significant.
Charles’ law
V/T is constant so y=mx
Any change at constant pressure is called an
isobaric change
When work is done to change the volume of a gas, energy must be transferred by heating to keep the pressure constant, and so the work done by the gas on a piston can be given by the equation
Work done = p(delta V)
The pressure law
the relationship between pressure p and the temperature T, in kelvins, is: p/T = constant so y=mx
Brownian motion
the motion of each particle is because it is bombarded unevenly and randomly by individual molecules. The particle therefore experiences forces due to these impacts, which change its magnitude and direction at random. So Brownian motion showed the existence of molecules and atoms
The Avogadro constant, NA, is defined as
the number of atoms in exactly 12g of the carbon 12 isotope= 6.023*10^-23
One atomic mass unit is
1/12th of the mass of a carbon 12 atom
One mole of a substance consisting of identical particles is defined as
the quantity of substance that contains NA particles
molarity is
The number of moles in a given quantity of a substance
The unit of molarity is the
the mol
The molar mass of a substance is
the mass of 1 mol of the substance. The unit of molar mass is kg/mol
The number of moles in a mass of a substance =
mass of substance/molar mass of substance
The number of molecules in a substance =
avagadros constant*mass of substance/molar mass of substance
An ideal gas is a gas that
obeys Boyle’s law
The three experimental gas laws can be combined to give
pV/T = constant for a fixed mass of ideal gas where T is the absolute temperature
The molar gas constant, R =
R = pV/T = 8.31J/Kmol for an ideal gas at absolute zero with a pressure of 101kPa
A graph of pV against temperature for n moles is
a straight line through absolute zero and has gradient equal to nR
So the combined gas law can be written as
pVm = RT where Vm = volume of 1 mol of ideal gas
Ideal gas equation
pV = nRT for n moles of ideal gas, where V = volume of the gas at pressure p and temperature T in kelvins
The mass of a substance is equal to
its molar mass * the number of moles
n =
pV/RT
Density of an ideal gas of molar mass M, p =
p = nM//V = pM/RT
In the equation pV = nRT, substituting the number of moles n in give
In the equation pV = nRT, substituting the number of moles n =N/NA gives pV=NkT where the Boltzmann constant k is R/NA and N is the number of molecules
For an ideal gas at constant pressure, its density is
inversely proportional to its temperature
k =
1.38*10^-23J/K
Boyles law explanation
the pressure of a gas at constant temperature is increased by reducing its volume because the gas molecules travel less distance between impacts at the walls due to the reduced volume. Therefore, there are more impacts per second, and so the pressure is greater
the pressure of a gas at constant temperature is increased if the volume is reduced because the gas molecules travel less distance between impacts at the walls due to the reduced volume hence there are more impacts per second and so greater pressure
Pressure law explanation
the pressure of a gas at constant volume is increased by raising its temperature. The average speed of the molecules is increased by raising the gas temperature. Therefore, the impacts of the molecules on the container walls are harder and more frequent so the pressure is raised.
the pressure of a gas at constant volume is increased by raising the temperature. The average speed of the molecules is increased by raising temperature so the impacts of the molecules on the container walls exert more force and are more frequent hence the pressure (F/A) increases
The root mean square speed of molecules =
the square root of (the sum of the squares of the individual molecules/number of molecules)
If the temperature of a gas is raised
its molecules move faster, on average. The root mean square speed of the molecules increases. The distribution curve becomes flatter and broader because the greater the temperature the more molecules there are moving at higher speeds.
Graph of number of molecules with speed v against speed v is
a normal distribution curve. Low temperature means the peak is stretched to the left. High temperature causes the peak to extend to the right.
For an ideal gas consisting of N identical molecules, each of mass m, in a container of volume V, the pressure p of the gas is given by the equation
pV = Nm(C(rms)^2)/3 where C(rms) is the root mean square speed of the gas molecules
For an ideal gas, its internal energy is due only to
the kinetic energy of the molecules of the gas
The mean kinetic energy of a molecule of a gas =
total kinetic energy of all the molecules/total number of molecules = 0.5mC(rms)^2, the higher the temperature of a gas, the greater the mean kinetic energy of a molecule of the gas
For an ideal gas at absolute temperature T
the mean kinetic energy of a molecule of an ideal gas = 1.5kT
where k=R/N(A)
The total kinetic energy of one mole =
NA *1.5kT = 1.5RT
The total kinetic energy of n moles of an ideal gas
= n*1.5RT = 1.5nRT
The total kinetic energy of n moles of an ideal gas =
1.5nRT - the internal energy for n moles of an ideal gas at temperature T (in kelvins)
The specific heat capacity is
the energy needed to raise the temperature of 1kg of that substance by 1K without changing state
The specific latent heat fusion of a substance is the energy needed to
change the state of unit mass of the substance from solid to liquid without change of temperature.
Vaporisation –> liquid to gas
Lowest possible temperature is called
absolute zero (0K = -273C), at 0K, all particles have the minimum possible kinetic energy – the particles are point masses. K = C + 273
Ideal gas equation
pV = nRT for n moles and as pV = NkT for N molecules
p= Pressure (Pa, Nm-2) V= Volume (cm3 , dm3 , m3 ) T= temperature (K, °C) R= Molar gas constant = 8.31 J/Kmol n= Number of moles
Number of particles in a mass of gas, N =
n*NA
Avogadro constant NA =
6.023*10^23
Boltzmann constant k
= R/NA = 8.31/6.02310^23 = 1.3810^-23J/K
Combine N=nNA and k= R/NA
Nk = nR
The molar mass of a substance is the mass of
1 mole of that substance
The molecular mass of a substance is the mass of
1 molecule of that substance
Assumptions made leading to derivation of 3pV=Nm(C(rms))^2
Randomly moving particles with range of velocities and direction
Particles are point masses – negligible volume
Perfectly elastic collisions
No intermolecular interaction between particles
Time of collision with container is less than time of flight between impacts
The root mean squared value is equal to the root mean value. Average molecular kinetic energy: 0.5mC(rms)^2 = 1.5Kt = 1.5(RT/NA)
Mean kinetic energy of a molecule of an ideal gas = 1.5kT
Total kinetic energy of n moles of an ideal gas = 1.5nRT
Boyle’s law: constant, explanation, equation, graphs
Temperature is kept constant (isothermal)
pV = constant
Graph of p against V is y=1/x
Graph of p against 1/V is y=x
at constant temperature, the pressure and volume of the gas are inversely proportional
Charles’ law: constant, explanation, equation, graphs
Pressure is kept constant (adiabatic)
V/T = constant
Graph of V against T is y=x
at constant pressure, the volume of a gas is directly proportional to its absolute temperature
Pressure law: constant, explanation, equation, graphs
Volume is kept constant
Graph of P against T is y=x
at constant volume, the pressure of a gas is directly proportional to its absolute temperature
The inversion tube experiment
tube, lead shots, glass rod replaced by thermometer: the gpe of an object falling in a tube is converted into internal energy when it hits the bottom of a tube. The tube is inverted each time the shots hit the bottom of the tube and the temperature of them is measured initally and after the inversions. For a tube of length L and inversions n, the loss of gpe = mgLn = the gain of internal energy = mc(b-a). Assuming all gpe lost is transferred to the internal energy of the lead shots we can rearrange to find c, the specific heat capacity.
How a liquid turns into a gas
When a liquid is heated at its boiling point, the molecules gain enough kinetic energy to overcome the bonds that hold them close together. The molecules therefore break away from each other to form bubbles of vapour in the liquid. The energy needed to vaporise a liquid is called latent heat of vaporisation.
Latent heat
Latent heat is released when a liquid solidifies. This happens because the liquid molecules slow down as the liquid cools until the temperature decreases to the melting point. At the melting point, the molecules move slowly enough for the force bonds to lock the molecules together. Some of the latent heat released keeps the temperature at the melting point until all the liquid has solidified. Latent/hidden heat supplied to melt a solid may be thought of as hidden because no temperature change takes place even though the solid is being heated.
Brake pads
The brake pads of a moving vehicle become hot if the brakes are applied for long enough time. The work done by the frictional force between the brake pads and the wheel heats the brake pads which gain energy from the kinetic energy of the vehicle. The temperature of the brake pads increases as a result, and the internal energy of each brake pad increases.
Molecules in an ideal gas have a …. The speed of an individual molecule changes when it … The distribution stays the same as long as …
Molecules in an ideal gas have a continuous spread of speeds. The speed of an individual molecule changes when it collides with another gas molecule. But the distribution stays the same as long as the temperature is the same.
