Internal Energy and Temperature

• Energy transfer occurs if: Work is done on one object by the other object

• Energy transfer occurs if: heating occurs due to a temperature difference between the objects

Internal Energy - the energy of an object due to the energy of its molecules due to their individual positions (potential) and movements (kinetic) - THE SUM OF THE RANDOM DISTRIBUTION OF THE KINETIC AND POTENTIAL ENERGIES OF ITS MOLECULES

• The internal energy due to temperature is sometimes referred to as thermal energy, but some internal energy is due to other causes

• Internal energy increases if energy is transferred via heating, or work is done on the object (e.g by electricity)

• If IE stays constant, it suggests that NO energy transfer by heating, and NO work done onto the object, OR energy transfer by heating and work done balance out

First law of Thermodynamics - The change in IE of an object = the total energy transfer due to work done and heating

• Increase PE, increase IE

• Increase KE, increase IE

• Higher IE, Higher Temp

If two objects are at the same temperature, they are at thermal equilibrium, and no overall energy transfer will take place

• Energy is transferred from hot objects to heat colder objects

Absolute 0 = 0K which is the lowest possible temperature

Triple point = 273K (0degrees), where water, exists as solid, liquid and gas

At absolute 0, the object has minimum internal energy. If gas pressure of a fixed mass is plotted against temperature on a graph, the graph always crosses the x-axis at -273degrees, no matter if the pressure is measured starting from ice point or steam point.

Specific Heat Capacity

The temperature rise of an object depends on its mass, the energy supplied to it, and the substance from which it is made

Specific Heat Capacity is the energy needed to raise the temperature of unit mass (1kg) of the substance by 1K, without changing its state

Q = mc(T - t)

Inversion tube experiment

• GPE of lead balls falling in a tube is converted into internal energy when it hits the bottom of the tube.

• The tube is inverted each time the lead spheres hit the bottom, and the temperature of the lead balls is measured initially and after a particular number of inversions.

if m is the mass of the lead balls, and L is the length of the tube

the loss of GPE for each inversion is mgL

so for n inversions, the loss of GPE total is mgLn

The gain in internal energy of the lead balls is mcΔt

so mcΔt = mgLn, and c = gLn/Δt

Electrical Methods

Metal of known mass

• a block of metal of known mass is placed into the insulating container

• a 12v electric heater is inserted into a hole drilled in the metal, and used to heat the metal by applying a measured amount of electrical energy.

• A thermometer inserted into a second hole is used to measure the temp rise - place a small amount of oil in the thermometer hole to improve the thermal contact between the thermometer and metal

energy supplied (electrical) = IxVxt

assuming no loss to the surroundings, mcΔt = IVt

so c = IVt/mΔt

Liquid

• A known mass of the liquid is used in an insulated calorimeter, of known mass and known specific heat capacity.

• A 12V electrical heater is placed in the liquid, and used to heat it directly

• A thermometer in the liquid measures the temperature rise

energy supplied (electrical) = IVt

Energy needed to heat the liquid = mass of liquid x c of liquid x Δt (m1 and c1)

Energy needed to heat the calorimeter = m(calorimeter)xc(calorimeter)xΔt (m2 and c2)

assuming no heat loss to surroundings - IVt = m1c1Δt + m2c2Δt

Continuous flow heating

• Electric shower - water flows over copper coils

• coils heated by electric heater

• so water is hotter at outlet than inlet

Electrical Energy produced per second IV = mc x ΔT/t

Change of State

If a solid is heated and heated - the temp increases until it melts (at its melting point if it is a pure substance)

When a solid is heated at its melting point, KE increases, so atoms vibrate so much they break free. So becomes a liquid. The energy needed is called Latent Heat of fusion.

The latent heat is released when the liquid solidifies again. As the liquid cools, the liquid molecules slow down, and at the melting point, the molecules are moving slow enough for the force bonds to lock the molecules together. Some of the Latent heat that is released keeps the temperature at the melting point until all has solidified.

Some solids vaporise when heated - sublimation

More energy is needed to vaporise a substance than melt it

Specific Latent Heat of Fusion - energy needed to change the state of 1kg of a substance from solid to liquid, without changing the temperature

Specific Latent heat of Vaporisation - energy needed to change the state of 1kg of a substance from liquid to vapour, without changing the temperature

Q = ml

Rise of temperature per second of a liquid = ΔT/Δt = P/mc where c is of the liquid

Rise of temperature per second of a solid = ΔT/Δt = p/mc where c is of the solid

Gases

• Pressure of gas = force per unit area that the gas exerts normally on the surface

Boyle’s Law

• pV = constant, for a fixed mass of gas at constant temperature

• An ideal gas is one that obeys Boyle’s law

Charles’ Law

• Plot volume of gas (y) against temperature, and extrapolate to find absolute zero

• At absolute zero, the volume is zero

• It can also be applied to pressure

• V/T = constant

• When work is done to change the volume of a gas, energy must be transferred (heating) to keep pressure constant, therefore W = p x change in Volume

Pressure Law

• P/T = constant

Ideal gas law

• Brownian motion - looking at smoke with a beam of light shown through under a microscope - the smoke particles move about unpredictably - so Brown discovered that gas molecules move with random and rapid motion

• This motion is caused as each molecule is impact with other molecules unevenly and randomly by individual molecules, and then the particle experiences a force due to this impact changing the magnitude and direction of motion

Avogadro Constant

• Equal volumes of gas at the same temperature and pressure contain equal numbers of molecules

• N(a) = Avogadro Constant - the number of atoms in exactly 12 grams of C-12

Molar Mass

• One mol of a substance is the quantity of a substance that has N(a) particles.

• The number of moles of a given substance = molarity (mol)

• Molar Mass is the mass of 1 mol of the substance (Kg/mol)

• Number of moles in the mass m(substance) = m(s)/M (where M is the molar mass and m is the mass of the substance)

• The number of molecules (N) in mass m(substance) = N(a) x m(s) all divided by M

• n = N/N(a)

Ideal Gas Equation

• Ideal gasses = OBEYS BOYLE’S LAW (cannot happen if pressure is too high - molecules become so close to each other that the molecules volume becomes significant)

• pV/T = constant

• Equal volumes of ideal gases, at the same temperature and and pressure contain equal number of moles

• A straight line graph of Pv against t is a straight line through absolute zero, and has gradient nR (number of moles x molar gas constant)

• pV = nRT (n = number of moles)

• pV = NkT (N = number of molecules)

Kinetic Theory of Gases

• Decrease volume = increase pressure because less volume means molecules travel less distance to collide and exert a force onto the wall, so more frequent collisions with wall, more force, more pressure.

• Increase Temperature = increase pressure because average speed of the molecules increases, so the impact of molecules onto the container walls are more frequent and forceful so pressure increases

Speeds

crms = (the sum of the speeds of the individual molecules/N)^1/2

mean speed = (the sum of the speeds of the individual molecules/N)

KINETIC THEORY WAS PRODUCED USING MATHEMATICS

GAS LAWS WHERE PRODUCED USING OBSERVATIONS IN A LAB

pV = 1/3 x N x m x crms²

Assumptions of an ideal gas

• volume of each molecule is negligible compared to the volume of the gas

• There are no forces acting between molecules

• They move in rapid, continual, random motion

• Collisions are elastic

• The time of a collision is much less than the time between collisions

DERIVATION OF THE KINETIC THEORY EQUATIONS CAN BE FOUND ON ONENOTE.