Thermal properties You should be able to: -state the basic definitions of calorimetry, such as specific heat capacity and specific latent heats of fusion and vaporization; -understand why temperature stays constant during a phase change; -outline methods for determining specific and latent heats experimentally; -solve calorimetry problems using Q=cmΔT and Q=mL; -state the factors that affect the rate of evaporation and distinguish between evaporation from boiling; -appreciate Boltzmann’s equation, the fundamental relationship between absolute temperature and the average kinetic energy of the molecules.

Specific heat capacity When heat is provided to a body, the temperature of a body will, in general, increase. The amount of heat needed to raise the temperature of a mass of one kilogram of a substance by one kelvin is called the specific heat capacity of the material. To raise the temperature of a mass m by ΔT kelvins, the amount of heat required is therefore Q = cm ΔT. The units of specific heat capacity are J/kgK

Heat capacity The product of mass times the specific heat capacity defines de heat capacity of a body C = mc, and therefore, Q = C ΔT. Heat capacity is the amount of heat required to change the temperature of a body by one kelvin. The concept of heat capacity is useful when a body consists of a number of parts of different specific heat capacities C = Mc + mc’

Example questions When a car brakes, an amount of heat equal to 112,500 J is generated in the brake drums. If the mass of the brake drums is 28 kg and their specific heat capacity is J/kgK, what is the change in their temperature? A radiator made out of iron has a mass of 45 kg and is filled with 23 kg of water. a)What is the heat capacity of the water-filled radiator? b)If heat is provided to the radiator at the rate of 450 W, how long will it take to the temperature to increase by 20°C?

Calorimetry Heat flows from hot bodies into cold bodies. The amount of energy (heat) lost by the hot body is equal to the amount of energy (heat) gained by the cold body. If there is interchange of heat between two or more bodies, then Q 1 + Q 2 + Q 3 +…+ Q N = 0

Example question A piece of iron of mass 200 g and temperature 300°C is dropped into 1 kg of water at 20°C. What will be the eventual temperature of the water? (Take c for iron as 470 J/kgK and for the water as 4200 J/kgK)

Phase states Kinetic theory basic assumptions: -All matter is composed of extremely small particles -All particles are in constant motion -If particles collide with neighbouring particles, they conserve their kinetic energy -A mutual attractive force exists between particles. There are four states (phases) of matter: solids, liquids, gases and plasma.

Macro and microscopic properties Characteristic SolidLiquidGas ShapeDefiniteVariable VolumeDefinite Variable CompressibilityAlmost incompressible Very slightly compressible Highly compressible DiffusionSmallSlowFast Comparative Density High Low CharacteristicSolidLiquidGas Kinetic energyVibrational Vibrational, rotational, some translational Mostly translational, higher rotational, higher vibrational Potential energy HighHigherHighest Mean molecular separation r0r0 r0r0 10r 0 Molecules per m Some macroscopic characteristics of solids, liquids and gases Some microscopic characteristic of solids, liquids and gases

Phase states Solids. The particles are closely packed and each particle is strongly bonded to its neighbour and is held fairly rigidly in a fixed position to give it definite shape in a crystalline lattice. Some patterns are disordered as is the case for ceramics, rubber, plastics and glass. These substances are said to be amorphous. The particles have vibrational kinetic energy in their fixed positions and the force of attraction between the particles gives them potential energy. Liquids. The particles are still closely packed and the bonding between particles is still quite strong. However, they are not held as rigidly in position and the bonds can break and reform. This infers that the particles can slowly and randomly move relative to each other to produce variable shape and slow diffusion. Particles in a liquid have vibrational, rotational and some translational kinetic energy due to their higher mean speeds. The potential energy of the particles in a liquid is somewhat higher than for a solid because the spacing between the particles is large.

Phase states Gases. The particles are widely spaced and the particles only interact significantly on collision or very close approach. Because of the rapid zig-zag motion of the particles, a gas will become dispersed throughout any container into which it is placed. Diffussion can occur readily. Gases are compressible because the particles are widely spaced at a distance much greater than the size of the particles. The much higger mean speeds are due to an increased translational kinetic energy of the particles. Gases have a much higher potential energy than liquids because the particles are much further apart.

Phase changes A substance can undergo changes of state or phase changes at different temperatures. Pure substances have definite melting and boiling points which are characteristic of the particular pure substance being examined. When the solid is heated the temperature begins to rise. When the temperature reaches its melting point, the substance begins to melt. Although heating continues the temperature of the solid-liquid mixture remains constant until all the substance has melted. Once all the substance has melted the temperature starts to rise until the liquid begins to boil. With continued heating the temperature remains constant until all the liquid has been converted to the gaseous state.

Molecular behaviour When the solid is heated the particles of the solid vibrate at an increasing rate as the temperature is increased. The vibrational kinetic energy of the particle increases. At the melting point a temperature is reached at which the particles vibrate with sufficient kinetic energy to break from their fixed positions and begin to slip over each other. As the solid continues to melt, more and more particles gain sufficient energy to overcome the forces beween particles and over time all the solid particles change to a liquid. The potential energy of the system increases. As heating continues the temperature of the liquid rises due to an increase in the vibrational, rotational and part translational kinetic energy of the particles. At the boiling point a temperature is reached at which the particles gain sufficient energy to overcome the interparticle forces present in the liquid and scape into the gaseous state. Continued heating at the boiling point provides the potential energy needed for all the molecules to be converted from a liquid to a gas. With further heating the temperature increases due to an increase in the kinetic energy of the gaseous molecules due to the larger translational motion.

Latent heat The heat required to melt one kilogram of substance at its melting point is called the latent heat of fusion, L f. The heat required to vaporise one kilogram of substance at its boiling point is called the latent heat of vaporisation, L v. Thus to melt or vaporise a quantity of mass m, we require a quantity of heat Q = m L f and Q = m L v, respectively. The latent heat unit is J/kg

Example question An ice cube of mass 25 g and temperature -10°C is dropped into a glass of water of mass 300 g and temperature 20°C. What is the temperature eventually? (Specific heat capacity of ice = 2200 J/kgK; latent heat of fusion of water = 334 kJ/kg.)

Evaporation and boiling A substance at a particular temperature has a range of kinetic energies. So in a liquid at any particular instant, a small fraction of the molecules will have kinetic energies considerably greater than the average value. If these particles are near the surface of the liquid, they may have enough kinetic energy to overcome the attractive forces of neighbouring particles and escape from the liquid as a vapour. The process of evaporation is a change from the liquid state to the gaseous state that occurs at a temperature below the boiling point.

Evaporation and boiling When the more energetic particles have escaped, the average kinetic energy of the remaining particles in the liquid has been lowered, which implies a lower temperature. This phenomenon is called evaporative cooling. A substance that evaporates rapidly is said to be a volatile liquid. A liquid’s volatility is controlled by a factor known as its equilibrium vapor pressure. Different liquids exert different vapour pressures that depend on the relative strengths of the intermolecular forces present in the liquids. SubstanceVapour pressure (kPa) Ether58.9 Chloroform19.3 Ethanol5.8 Water2.3 Mercury0.0002

Kinetic model of an ideal gas The properties of gases can be understood in terms of a simple but effective mechanical model. The gas consists of a very large number of molecules moving randomly about with a range of speeds and colliding with each other and the container walls. We can make a model of this by making certain assumptions: 1.A gas consists of a large number of molecules. 2.Molecules move with a range of speeds. 3.The volume of the molecules is negligible compared with the volume of the gas itself. 4.The collisions of the molecules with each other and the container walls are elastic. 5.Molecules exert no forces on each other or the container except when in contact. 6.The duration of collisions is very small compared with the time between collisions. 7.The molecules obey Newton’s laws of mechanics.

Boltzmann Law Using this assumptions: Where the speed v is defined by We call v the root mean square speed o rms speed. It is not the average speed of the molecules. k is called the Boltzmann constant and has a value of 1.38 x J/K The absolute temperature is a measure of the average kinetic energy of the molecules of a substance.

Molecular explanation of pressure The pressure of a gas originates from the collisions of the molecules with the walls of its container. At every collision, each molecule has its momentum changed and so a force acts from the wall onto the molecule. By Newton’s third law, the molecule exerts an equal and opposite force on the wall. The total force due to all the colliding molecules divided by the area over which the force acts gives the pressure of the gas.

Boyle-Mariotte law The parameters P, V, T and n are related to each other. The equation relating them is called the equation of state. At constant temperature and with a constant quantity of gas, pressure is inversely proportional to volume, that is PV = constant.

Charles law At constant pressure, it is found that the volume increases uniformly with temperature V/T = constant

Gay-Lussac law At constant volume, it is found that the volume increases uniformly with temperature P/T = constant

The equation of state If we combine these three laws, we see that PV/T = constant It was also discovered that PV/T = n x constant It was found that this constant has the same value for all gases R = 8.31 JK -1 mol -1 Then, PV = nRT or PV = NkT k = R/N A