An Introductory Course in Waterloo Collegiate Institute SPH3U Thermal Physics An Introductory Course in Thermodynamics Waterloo Collegiate Institute

Thermal Physics electrons and holes in semiconductors converting energy into work magnetism thin films and surface chemistry thermal radiation (global warming) and much more…

Some Definitions Absolute Zero: the lowest possible temperature, at which all molecular motion would cease and a gas would have zero volume. Calorie: the amount of heat required to raise the temperature of one gram of water by one Celsius degree. Calorimeter: device which isolates objects to measure temperature changes due to heat flow. Celsius (C): temperature scale in which the freezing point of water is 0 and the boiling point of water is 100 Convection: heat transfer by the movement of a heated substance, due to the differences in density. Conduction: heat transfer from molecule to molecule in substances due to differences in temperature.

Heat Heat, represented by the variable Q, is a type of energy that can be transferred from one body to another Heat is measured in Joules Energy must be transferred in order to be called heat. (So heat may be gained or lost, but not possessed. It is incorrect to say, “a gas has 4000 J of heat” Internal energy: The sum of the energies of all of the molecules in a substance. Represented by the variable U (for example: the total of the Kinetic and Potential energy at the molecular level is called the Internal Energy of the system. U=KE+PE) Temperature: Related to the average kinetic energy per molecule of a substance.

What is Heat? Up to mid-1800’s heat was considered a substance -- a “caloric fluid” that could be stored in an object and transferred between objects. After 1850, kinetic theory. A more recent and still common misconception is that heat is the quantity of thermal energy in an object. The term Heat (Q) is properly used to describe energy in transit, thermal energy transferred into or out of a system from a thermal reservoir … (like cash transfers into and out of your bank account) Q U Sign of Q : Q > 0 system gains thermal energy Q < 0 system loses thermal energy W > 0 work done on system W < 0 work done by the systems So we give Q + W a name: The Internal Energy

Still More Heat We will be discussing three states of matter (solid, liquid, and gas). The molecules of a solid are fixed in a rigid structure. The molecules of a liquid are loosely bound and may mix with one another freely. (While a liquid has a definite volume, it still takes the shape of its container. The molecules of a gas interact with each other slightly, but usually move at higher speeds than that of solid of liquid. In all three states of matter the molecule are moving and therefore have Kinetic Energy. But, they also have Potential Energy due to the bonds between them. The sum of the potential and kinetic energies of the molecule of the substance is also known as its Internal Energy. When a warmer substance comes in contact with a cooler substance, some of the kinetic energy of the molecules in the warmer substance is transferred to the cooler substance. The energy representing this kinetic energy of the molecule that is transferred from the warmer to the cooler substance is called heat energy.

What is temperature? A mercury thermometer The mercury rises up the tube as it expands. This is movement. An object (say, a cup of hot chocolate) The mercury is gaining (internal) energy from the hot chocolate. This transfer of energy is what we call heat. When the transfer stops, the objects are in thermal equilibrium.

Temperature Scales Celsius (0C) Zero defined by an ice-water bath at 1 atm. Unit defined by water-steam (100ºC) at 1 atm. Kelvin (absolute K) Zero defined by absolute zero, but we cannot reach that temperature experimentally 273.16 K defined by the triple-point of water (0.01ºC at 4.58 mm of mercury, water can exist in all three states of matter) Unit is the same as the Celsius scale Fahrenheit (0F) Zero and unit based on salt-water, water freezes at 32 0F and boils at 212 0F ) Fahrenheit scales, used a scale point of 98 for body temp, goofed, became 98.6. didn’t want negatives

Converting Between the Scales From Celsius to Kelvin: From Fahrenheit to Celsius:

Example You place a small piece of melting ice in your mouth. Eventually, the water all converts from the ice at T1=32.00 0F to body temperature, T2 =98.60 0F. Express these temperatures as 0C and K. Plan: We convert Fahrenheit to Celsius temperature, then from Celsius to Kelvin

Mechanical Equivalent of Heat James Joule showed that mechanical energy could be converted to heat and arrived at the conclusion that heat was another form of energy. He showed that 1 calorie (c) of heat was equivalent to 4.184 J of work. (that is 1 calorie is defined as the heat needed to raise the temperature of 1 gram of water 1 0C) 1 cal = 4.184 J Kilocalorie(C) – the amount of heat needed to raise the temperature of 1,000 grams of water by 1 °C. (Used with food, Food calories (C) are determined by burning the food and measuring the amount of energy that is released.) British Thermal Units (BTUs) are the amount of heat to raise one pound of water by 1 °F.

Boiling Point, Melting Point & Condensation point Substances warm up when absorbing thermal energy. Ex. a solid absorbing enough thermal energy to melt (melting point). Substances cool down when giving off thermal energy. Ex. a liquid giving off enough energy to freeze (freezing point which usually = melting point) The boiling point of a substance can also be called the condensation point (when a gas loses enough thermal energy to become a liquid)

Thermal Energy & Temperature Objects made of the same material but with different masses and the same temperature will not have the same thermal energy The object with less mass has less thermal energy since thermal energy is the total kinetic and potential energy. Conduction – transfer of thermal energy when warmer objects are in contact with cooler objects. Convection – transfer of thermal energy through a fluid (air or liquid) that rises when it is hotter and less dense and cools and sinks when more dense pushing warmer, less dense further upward. (ie. A convection current) Radiation – the movement of thermal energy as electromagnetic waves.

Specific Heat Capacity Different substances absorb thermal energy at different rates. Ex. Heating water will take longer than heating the same amount of oil. The oil will also cool off faster. Specific Heat Capacity (SHC or c) is the amount of energy in joules required to increase the temperature of 1 kg of a substance by 1°C Units for SHC or c is J/(kg°C ) https://www.youtube.com/watch?v=BclB8UaSH4g

Water’s high specific heat capacity means it takes a great deal more energy to raise its temperature by 1°C then it would to raise the temperature of the same mass of another substance such as aluminum by one degree. This means lakes, oceans, atmospheric moisture are have very significant roles in moderating our temperature.

Heat Transfer and Temperature Change The change in temperature that a substance experiences depends upon two things: its identity (specific heat) and the amount of material (mass). The equation that connects the amount of heat, Q, and the resulting temperature change , T in 0C, is: Where Q is the quantity of heat (calories) m is the mass of the sample in grams and c is the intrinsic property called specific heat capacity in 1 cal/g°C. Note: that positive Q is interpreted as heat coming in (T is positive, so T increases), while negative Q corresponds to heat going out (T is negative, so T decreases).

Q = m c ΔT Given: ∆Q =504 kJ = 504 000 J m=11.5 kg c = 4200 J /kg °C A bucket containing 11.5 litres of cold water at 10°C is taken into a house at a warmer temperature and left inside until it has reached thermal equilibrium with it new surroundings. If 504 kJ of energy is absorbed from the surroundings to heat the water, what is the temperature of the room? Given: ∆Q =504 kJ = 504 000 J m=11.5 kg c = 4200 J /kg °C T = ? Q = m c ΔT ΔT = Q ÷ mc = 504 000 J ÷ (11.5 kg)(4200J/kg °C) = 10.4 °C Room Temp = 10.4 °C + 10 °C = 20.4 °C

The Heat lost by the metal (-Q) is Heat gained by the water (+Q) A 60.0g sample of metal is heated to 100.0°C before being placed in 200.0mL of water with an initial temperature of 10.0°C. The metal-water combination reaches a final temperature of 15.4°C. Determine the identity of the metal. (c water = 4200 J/kgᵒC) The Heat lost by the metal (-Q) is Heat gained by the water (+Q) mmcmΔT + mwcw ΔT = 0 Which variable, when calculated will allow us to determine what the metal is that was dropped in the water?

Looks like it is Aluminum 0.060 kg -84.6 °C 5.4 °C 15.4 °C 0 = mmcmΔT + mwcw ΔT - mmcmΔT = mwcw ΔT Looks like it is Aluminum -(0.060kg) cm(-84.6°C) = 0.20kg (4200J/kg°C) (5.4 °C) Cm = 894 J/kg °C Since we know the specific heat capacity of the metal, we can identify the metal from a table!

Heat Transfer Example During a bout with the flu an 80. kg man ran a fever of 39.0 0C instead of the normal body temperature of 37.0 0C. Assuming that the human body is mostly water (c=1cal/g 0C), how much heat, in calories and Joules, is required to raise his temperature by that that amount? We could also use:

Internal energy is stored in bonds between atoms and molecules Solids have the strongest bonds Energy is required to break them to a liquid When energy is absorbed to break those bonds the energy is used for the separation of the atoms instead of increasing the temperature (average kinetic energy of the atoms. It takes as much energy to melt 1 g of ice as it does to raise the temperature from 0ᵒC to 80ᵒC .

Q Qf Qv Latent heat Latent heat Latent heat of Fusion the total thermal energy absorbed or released when a substance changes state: measured in Joules. Latent heat of Fusion Qf the amount of thermal energy required to change a solid into a liquid, or a liquid into a solid. Latent heat Vaporization Qv the amount of thermal energy required to change a liquid into a gas or a gas into a liquid.

Heating Curve

Heating Curve

Heating Curve & Quantity of Heat (Q)

Q = m Lf Q = m Lv Specific Latent Heat Specific Latent Heat (L): the amount of thermal energy required for 1kg of a substance to change from one state into another; measured in Joules per kilogram. L is a constant for a given material. Specific Latent Heat of Fusion (Lf): the amount of thermal energy required to melt or freeze 1kg of a substance in Joules / kilogram. Latent heat (Q) during freezing or melting is calculated using m & Lf: Q = m Lf Specific Latent Heat of Vaporization (Lv): the amount of thermal energy required to evaporate or condense 1kg of a substance in Joules per kilogram. Latent heat (Q) during boiling or condensation is calculated using m & Lv : Q = m Lv

Heat Transfer and Phase Changes Consider an ice cube. Since water freezes at 0 0C, the temperature of the ice cube is 0 0C. If we add heat to the ice, its temperature does not rise. Instead the thermal energy absorbed by the ice goes into loosening the intermolecular bonds of the ice, thereby transforming it into a liquid. The temperature remains at 0 0C. In each phase change (solid to liquid, liquid to gas), absorbed heat causes no temperature change so Q=mcT does not apply. The equation we use is: Where L is the latent heat of transformation (solid to liquid, or vice versa L is latent heat of fusion. From liquid to gas, L is called latent heat of vaporization). This equation tells us how much heat must be transferred in order to cause a sample of mass m to undergo a phase change.

Ex. How much thermal energy is released by 652 g of molten lead when it changes into a solid given LF=2.5x104 J/Kg? Lead: liquid  solid Given: m = 652 g = 0.652 kg Lf = 2.5 x 104 J/kg Q = m Lf Q = m Lf = (0.652 kg) (2.5 x 104 J/kg) = 1.6 x 104 J

Latent Heat & Energy Absorption Question: How much thermal energy is released when 500.0g of steam at 100°C condenses and cools to 50°C? Break the problem into its two parts and add them together! 1) The heat given off during the temperature change using Q = mcΔT The heat given off during the phase change using Q = mL Add the two values of Q together

How much thermal energy is released when 500 How much thermal energy is released when 500.0g of steam at 100°C condenses and cools to 50°C? Q1 = mcΔT = (0.500kg)(4200 J/kg°C)(50°C - 100°C) = - 105 000 J = - 1.05 x 105 J Q2 = m Lv = (0.500kg)(-2.3 x 106 J/kg) = - 1.15 x 106 J Qtotal = Q1 + Q2 = - 1.05 x 105 J + (- 4.6 x 106 J) = - 1.3 x 106 J Given: m = 500.0g = 0.5000 kg T1= 100°C T2= 50°C c = 4200 J/kg°C Lv = 2.3 x 106 J/kg

Example on Temperature and Phase You want to cool 0.25kg of water, initially at 25 0C, by adding ice, initially at -20 0C. How much ice should you add so that the final temperature will be 0 0C with all the ice melted [cwater = 4190 J/kg K, cice=2100 J/kg K, L=334000J/kg]? The ice and water are the objects that exchange heat. The water undergoes a temperature change only, while the ice undergoes both a temperature and phase change. We require the mass of the ice. Note: Qabsorbed + Qreleased = 0 Let’s first determine the negative heat added to the water. For Ice, first we determine the heat needed to warm the ice.

Example on Temperature and Phase You want to cool 0.25kg of water, initially at 25 0C, by adding ice, initially at -20 0C. How much ice should you add so that the final temperature will be 0 0C with all the ice melted [cwater = 4190 J/kg K, L=334000J/kg]? For Ice, now we need the heat to phase shift it from solid to liquid. The sum of these quantities must be zero