CHAPTERS 13-15 Thermal Energy & States of Matter

Kinetic theory of gases Particles in a hot body have more kinetic energy than those in a cold body; as temperature increases, kinetic energy increases.

IDEAL GASES An ideal gas is made up of a large number of gas molecules N each with mass m moving in random directions with a variety of speeds. The gas molecules are separated from each other by an average distance that is much greater than the molecule's diameter. The molecules obey laws of mechanics, interacting only when they collide. Collisions between the walls of the container or with other gas molecules are assumed to be perfectly elastic.

Entropy disorder the higher the temperature, the more disorder (or entropy) a substance has

Temperature measure of an object’s kinetic energy; temperature measures how hot or how cold an object is with respect to a standard Temperature is a property of a system that determines whether the system will be in thermal equilibrium with other systems.

Temperature Scales Celsius (or Centigrade, though in the United States the Fahrenheit scale is common. Celsius scale, the freezing point of water corresponds to 0°C and the boiling point of water corresponds to 100°C. Fahrenheit scale, the freezing point of water is defined to be 32°F and the boiling point 212°F. It is easy to convert between these two scales by remembering that 0°C = 32°F and that 5°C = 9°F. The Kelvin scale is based upon absolute zero (-273.15 °C), or 0 K.

Triple Point The triple point of water serves as a point of reference. It is only at this point (273.16 °K) that the three phases of water (gas, liquid, and solid) exist together at a unique value of temperature and pressure.

Molecular Interpretation of Temperature kinetic theory: The concept that matter is made up of atoms in continual random motion. In an ideal gas, there are a large number of molecules moving in random directions at different speeds, the gas molecules are far apart, the molecules interact with one another only when they collide, and collisions between gas molecules and the wall of the container are assumed to be perfectly elastic. The average translational kinetic energy of molecules in a gas is directly proportional to the absolute temperature. If the average translational kinetic energy is doubled, the absolute temperature is doubled.

EQUATIONS KEav = 1/2 mvav2 = 3/2 kT T - temperature in Kelvin k - Boltzmann's constant k = 1.38 x 10-23 J/K The relationship between Boltzmann's constant (k), Avogadro's number (N), and the gas constant (R) is given by: k = R/N

relationship between pressure and the kinetic theory The pressure exerted by an ideal gas on its container is due to the force exerted on the walls of the container by the collisions of the molecules with the walls of area “A”. The collisions cause a change in momentum of the gas molecules. The pressure is directly proportional to the square of the average velocity. Because average kinetic energy is directly proportional to the temperature, pressure is also directly proportional to the temperature (for a fixed volume).

EQUATIONS PV = 2/3 N (1/2 mvav2) The higher the temperature, according to kinetic theory, the faster the molecules are moving, on average. rms speed The square root of the average speed in the kinetic energy expression is called the rms speed. vrms = (3RT/M)1/2 where R is the ideal gas constant, T is temperature in Kelvin, and M is the molecular mass

Heat (symbol is Q; SI unit is Joule) amount of thermal energy transferred from one object to another due to temperature differences Q = m c DT where m is mass in kg c is specific heat of the material DT = Tf - Ti in °C

Heat with moles of gas   Typically, moles of gas are given instead of the mass of the gas. In that case, heat can be calculated using            Q = n c DT           where n is the number of moles           c is the molar specific heat of the gas

Specific Heats of Gases   molar specific heats of gases are expressed in terms of constant pressure or constant volume conditions. In the case of a constant volume process, the constant would be expressed as cv the case of a constant pressure process, the constant would be expressed as cp. Use these constants in Q = n c DT.

Mechanical Equivalent of Heat James Joule described the reversible conversion of heat energy and work. The calorie is defined as the amount of energy needed to raise the temperature of one gram of water at 14.5° one degree Celcius. The SI unit for work and energy is the Joule. 1 calorie = 4.184 J

Specific heat (c) a characteristic of a material the amount of energy (measured in Joules) that must be added to raise the temperature of one kilogram of the material one degree Celcius or one Kelvin specific of heat of water: c = 4180 J/kg K (at a temperature of 15°C and a pressure of 1 atmosphere)

the units J/kg K are the same as J/kg °C Substance specific heat aluminum 900 J/kg K silver 230 J/kg K zinc 388 J/kg K copper 390 J/kg K ice 2060 J/kg K lead 128 J/kg K iron 450 J/kg K steam 2020 J/kg K glass 837 J/kg K

What good is specific heat? Notice that the specific heat of water is very high - higher than ice and steam. Water has a very high specific heat, meaning that it heats slowly and cools slowly. The specific heat of a material yields information about how the material heats and cools. If you add heat to two materials, the one with the lowest specific heat will show the greatest temperature change. If you cool two materials ten degrees, the material with the greatest specific heat loses the most energy.

Measurement of heat capacity (c) a substance is heated over a period of time. If V is the voltage, i is the current, Dt is the change in time in seconds, DT is the difference in temperature, and n is the number of moles, the specific heat capacity can be found by

Molar heat capacity The molar heat capacity is based upon the number of moles of the substance. Heat can be expressed in terms of molar heat capacity by: Q = n C DT

Energy transfer mechanisms: conduction (solids)-KE transfer due to collisions of particles; heat transfer occurs only when there is a difference in temperature Thermal Conductivity It is found experimentally that the heat flow per unit of time (DQ/Dt)is proportional to the corss-sectional area of the object (A), the distance (d) between the two ends of the object, the temperatures of each end of the object (T1 and T2), and a proportionality constant, k, called the thermal conductivity of the substance. DQ/Dt = kA(T1 - T2)/d Substances that have large values for k are good thermal conductors. Those with low values for k are good insulators. convection (fluids)-KE transfer due to movements of fluids over large distances caused by different densities at different temperatures

Energy transfer mechanisms: radiation-energy transfer through a vacuum. Conduction and convection require the presence of matter. Radiation consists of electromagnetic waves. Stefan-Boltzmann equation The rate at which an object radiates energy is proportional to the fourth power of the Kelvin temperature, T. DQ/Dt = seAT4 where A is the area s is Stefan-Boltzmann constant = 5.67 x 10-8 W/m2 K4 e is the emissivity (a number between 0 and 1) Very black surfaces has emissivities close to 1 Very shiny surfaces have emissivities close to 0. A good absorber of radiation is also a good emitter of radiation.

Which way does it go? When different parts of an isolated system are at different temperatures, heat will flow from the part at a higher temperature to that at the lower temperature until they are at thermal equilibrium

Law of heat exchange the sum of heat losses and gains in a closed system is zero. When two bodies of unequal temperature are mixed, the cold body absorbs heat (raising its temperature) and the hot body loses heat (lowering its temperature) until an equilibrium temperature is reached. Thermal equilibrium exists when two objects that are in thermal contact with one another no longer affect each other's temperature. Qloss + Qgain = 0 Objects are in thermal equilibrium when they are at the same temperature.

Calorimeter device used to measure changes in thermal energy

Changes of State The three most common states of matter :solid, liquid, and gas. When heat is added to a substance; The temperature can increase or the material can change to a different state. There is a fourth state of matter - plasma. A plasma is a state of matter in which atoms are stripped of their electrons. In a plasma, atoms are separated into their electrons and bare nuclei.

What happens to the energy When a material changes phases from solid to liquid or from liquid to gas, a certain amount of energy is absorbed (in the reverse process, the heat is given off). Let's look at ice (a solid) at a temperature of -5°. When heat is added to ice, its temperature increases until it reaches 0°. At this point, ice begins to melt--it changes its state from a solid to a liquid. The temperature remains constant at 0° until all the ice has melted. Now we have water at 0°. As heat is added to the water, its temperature increases until it reaches 100°. At this point, the water begins to boil, changing its state from liquid to gas. The temperature remains constant at 100° until all the water boils, turning into steam. Now we have steam at 100°. If you continue to add heat, the temperature of the steam begins to increase.

Latent heat of fusion, (Hf or Lf) amount of energy needed to change 1 kg of a substance from a solid to a liquid. for water, Hf = 333,000 J/kg (333 x 103 J/kg) or 3.33 x 105 J/kg

Latent heat of vaporization,(Hv or Lv) amount of energy needed to change 1 kg of a substance from a liquid to a gas. for water, Hv = 2,260,000 J/kg K (or 2.26 x 106 J/kg) or 22.6 x 105 J/kg

during phase change, the amount of heat given off or absorbed is found… Q = m H or Q = mL (where L is the latent heat) where m is mass in kg and H is heat of transformation. No temperature change occurs at a phase change.

Example: How much heat is added to 10 kg of ice at -20°C to convert it to steam at 120°C? 1. draw a diagram 2. calculate the heat required

SOLUTION The amount of heat added to change ice at -20°C to steam at 120°C is given by: Q = (10 kg)(2060 J/kg°C)(0°C + 20°C) + (10 kg)(333 x 103 J/kg) + (10 kg)(4180 J/kg°C)(100°C - 0°C) + (10 kg)(2.26 x 106 J/kg) + (10 kg)(2020 J/kg°C)(120°C - 100°C)

Experimentally determining the amount of heat added You cannot directly measure the amount of heat added in Joules. Graph temperature vs time. If you know the rate at which heat is being added and how long it is added, you can determine the amount of heat added. If you use an electric device to heat the substance, you can determine how much electrical energy was transferred to the substance knowing that: EE (electrical energy) = Pt = Vit P is power in watts (remember, 1 W=1 J/sec) t is time V is voltage i is current You can also convert gravitational potential energy (GPE) into thermal energy. Remember: work and energy are equivalent!

PHASE CHANGES Sublimation a solid changes directly to a gas without passing through the liquid phase. Evaporation Evaportation can be explained in terms of the kinetic theory. The fastest moving molecules in a liquid escape from the surface, decreasing the average speed of those remaining. When the average speed is less, the absolute temperature is less. Evaporation is a cooling process. Boiling When the temperature of a liquid equals the point where the saturated vapor pressure equals the external pressure, boiling occurs.

Thermal Expansion Most substances expand when heated and contract when cooled. The exception is water. The maximum density of water occurs at 4°. This explains why a lake freezes at the surface, and not from the bottom up. If water at 0°C is heated, its volume decreases until it reaches 4°C. Above 4°C, water behaves normally and expands in volume as it is heated. Water expands as it is cooled from 4°C to 0°C and expands even more as it freezes. That is why ice cubes float in water and pipes break when the water inside of them freezes. The change in length in almost all solids when heated is directly proportional to the change in temperature and to its original length. A solid expands when heated and contracts when cooled: The length of a material decreases as the temperature decreases AND increases as the temperature increases. DL = a L DT where L is the length of the material a is the coefficient of linear expansion DT is the temperature change in ° C

WHAT ABOUT A GAS? The volume of a gas decreases as the temperature decreases The volume increases as the temperature increases. DV = b V DT where V is the volume of the material b is the coefficient of volume expansion DT is the temperature change in °C

Expansion values material coefficient of linear expansion coefficient of volume expansion aluminum 25 x 10-6 /°C 75 x 10-6 /°C brass 19 x 10-6 /°C 56 x 10-6 /°C iron or steel 12 x 10-6 /°C 35 x 10-6 /°C lead 29 x 10-6 /°C 87 x 10-6 /°C concrete 36 x 10-6 /°C gasoline   950 x 10-6 /°C mercury 180 x 10-6 /°C ethyl alcohol 1100 x 10-6 /°C water 210 x 10-6 /°C air 3400 x 10-6 /°C

Thermal Stress In many buildings and roads, the ends of a beam or other material are held rigidly fixed. If the temperature should change, large compressive or tensile forces develop, called thermal stresses. Elastic modulus can be used to calculate these thermal stresses.

ASSIGNMENT PROBLEM SOLVING – THERMAL ENERGY SAMPLE PROBLEMS;AP HEAT SAMPLE PROBLEMS OPTIONAL EXTRA PRACTICE: STATES OF MATTER SAMPLE PROBLEMS