PHYSICS 220 Lecture 24 Heat Textbook Sections 14.4 14.5 Lecture 25 Purdue University, Physics 220 1
Exam 2 Average: 96.7 out of 150 Std Dev: 30.5 Lecture 25 Purdue University, Physics 220 2
Overview Last Lecture Thermal Expansion ΔL = α L 0 ΔT (linear expansion) ΔV = β L 0 ΔT (volume expansion) Kinetic Theory of Monatomic Ideal Gas <K tr >=3/2k B T Today Heat Specific Heat Phase Transitions Lecture 25 Purdue University, Physics 220 3
Quiz 1) A pendulum is made from an aluminum rod with a mass attached to its free end. If the pendulum is cooled does the pendulum's period A) increase B) decrease C) stay the same 2) A steel tape measure is marked in such a way that it gives accurate length measurements at a normal room temperature of about 20 C. If this tape measure is used outdoors on a cold day when the temperature is 0 C, are its measurements A) too long B) too short C) accurate Lecture 25 Purdue University, Physics 220 4
Internal Energy Energy of all molecules including Random motion of individual id molecules l <K tr > = 3/2 k T for ideal gas Vibrational energy of molecules and atoms Chemical energy in bonds and interactions DOES NOT INCLUDE Macroscopic motion of object Potential energy due to interactions with other objects Lecture 25 Purdue University, Physics 220 5
Heat Definition: Flow of energy between two objects due to difference in temperature Note: similar to WORK Object does not have heat (it has energy) Units: calorie Amount of heat needed to raise 1g of water 1ºC 1 Calorie = 1 kcal = 1000 cal = 4186 Joules Heat flows from a system at higher temperature to one at lower temperature Lecture 25 Purdue University, Physics 220 6
Heat The energy that flows between the systems is called heat or heat energy Heat is energy that passes from one system to another by virtue of a temperature difference The terms heat and heat energy are often used interchangeably In physics, they always refer to the transfer of energy between systems According to the principle of conservation of energy, the amount of heat energy that leaves system 1 must equal the amount of heat energy that enters system 2 The transfer can take place in different ways The direction of the transfer depends only on the temperature difference Lecture 25 Purdue University, Physics 220 7
Units of Heat The SI unit of heat is the same as for energy, the Joule (J) A unit called the calorie is widely used for heat 1 cal = 4.186 J The Calorie, with an uppercase C, is used to measure the energy content of food 1 Calorie = 1000 calories So 1 food Calorie is a kcal Lecture 25 Purdue University, Physics 220 8
Heat and Mechanical Energy James Joule measured the mechanical equivalent of heat energy The apparatus he used is similar to the one shown As the mass fell, its potential energy rotated the paddle, raising the temperature of the liquid Joule could then relate the mechanical energy to the heat energy Lecture 25 Purdue University, Physics 220 9
Heat Capacity and Specific Heat Heat capacity is the ratio between the heat energy added to a system and the resulting change in temperature Q heat capacity = ΔTT Specific heat takes into account the size (mass) of the system specific heat = c = Q mδt Lecture 25 Purdue University, Physics 220 10
Specific Heat Heat adds energy to object/system IF system does NO work then: Heat increases internal energy: Q = ΔU Heat increases temperature: t Q = C ΔTT Q = c m ΔT Heat required to increase temperature depends on amount of material (m) and type of material (c) Q = cmδt : Cause = inertia x effect (just like F=ma) cause = Q effect = ΔT inertia = cm (mass x specific heat capacity) c specific heat ΔT = Q/cm (just like a = F/m) Lecture 25 Purdue University, Physics 220 11
Exercise After a grueling work out, you drink a liter of cold water (0 C). How many Calories does it take for your body to raise the water up to body temperature peaueof 36C C? A) 36 B) 360 C) 3,600 D) 36,000 1 liter = 1,000 grams of H 2 0 1000 g x 1 calorie/(gram degree) x (36 degree) = 36,000 calories 36,000 calories = 36 Calories! Lecture 25 Purdue University, Physics 220 12
Question Suppose you have equal masses of aluminum and copper at the same initial temperature. You add 1000 J of heat to each of them. Which one ends up at the higher final temperature A) aluminum B) copper C) the same Substance c in J/(kg-C) aluminum 900 copper 387 iron 452 lead 128 human body 3500 water 4186 ice 2000 ΔT =Q/cm Lecture 25 Purdue University, Physics 220 13
ILQ Two insulated buckets contain the same amount of water at room temperature. Two blocks of metal of the same mass, both at the same temperature, are warmer than the water in the buckets. One block is made of aluminum (c=0.9) and one is made of copper. You put the aluminum block into one bucket of water, and the copper (c=0.385) block into the other. After waiting a while you measure the temperature of the water in both buckets. Which is warmer? A) The water in the bucket containing the aluminum block B) The water in the bucket containing the copper block C) The water in both buckets will be at the same temperature Since aluminum has a higher specific heat than copper, you are adding more heat to the water when you dump the aluminum in the bucket (Q=mcΔT). Lecture 25 Purdue University, Physics 220 14
Specific Heat for Ideal Gas Monatomic Gas (single atom) Translational kinetic energy only At constant Volume work = 0 Q = ΔU = 3/2 nrδt C V = 3/2 R = 12.5 J/(K mole) Diatomic Gas (two atoms) Can also rotate C V = 5/2 R = 20.8 J/(K mole) Lecture 25 Purdue University, Physics 220 15
Latent Heat As you add heat to water, the temperature increases for a while, then it remains constant, t despite the additional heat! 100 o C Substance L f (J/kg) L v (J/kg) water 33.5 x 10 4 22.6 x 10 5 f=fusion T v=vaporization water water changes temp to steam rises (boils) Latent Heat Q added to water steam temp rises Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid-gas). Q = m L Lecture 25 Purdue University, Physics 220 16
Phases of Matter There are three states t of matter: Solid Liquid Gas Lecture 25 Purdue University, Physics 220 17
Solids The atoms in many solids are arranged in an orderly and repeating pattern called a crystalline lattice Each atom is held in place by the forces exerted by neighboring atoms These forces are a result of chemical bonds within the solid The atoms actually vibrate about their positions as simple harmonic oscillators An amorphous solid has atoms arranged without the repeating structure found in a crystal Lecture 25 Purdue University, Physics 220 18
Liquids The atoms in a liquid are not held in fixed locations by the forces of neighboring atoms The atoms are able to move about The atoms adjacent to a particular atom are not likely to be adjacent a short time later This motion helps liquids to flow Although the bonds between neighboring atoms do not persist, there is still potential energy associated with the forces between the molecules Lecture 25 Purdue University, Physics 220 19
Gases In some ways, a gas is similar to a liquid The molecules are able to move over long distances The density of a gas is generally much lower than that of a liquid The spacing between the molecules of a gas is larger The magnitude of the intermolecular force, and therefore potential energy, is much smaller Most of the mechanical energy in a gas is found in the kinetic energies of its molecules Lecture 25 Purdue University, Physics 220 20
Internal Energy The mechanical energy of the molecules in a system is called the internal energy of the system Denoted by U The internal energy of a system is the sum of all potential energies associated with all the intermolecular bond plus the kinetic energies of all the molecules The value of U increases as we go from solid to liquid to gas In general, the internal energy of all systems increases as the temperature is increased Lecture 25 Purdue University, Physics 220 21
Phase Transitions A phase transition occurs whenever a material is changed from one phase, such as the solid phase, to another phase, such as the liquid phase. Phase transitions occur at constant temperature. The latent heat of vaporization L V is the heat per unit mass that must flow to change the phase from liquid to gas or from gas to liquid. Fusion occurs when a liquid id turns into a solid. Evaporation occurs when a liquid turns into a gas. Sublimation occurs when a solid changes directly to a gas without going into a liquid form. Lecture 25 Purdue University, Physics 220 22
Phase Changes The transformation of a solid to a liquid, a liquid to a gas, etc. is called a phase change Phase changes can be produced by changing the temperature or by changing g the pressure of the system A phase diagram shows the phases found at different temperatures and pressures Lecture 25 Purdue University, Physics 220 23
Phase Changes, cont. Phase diagrams show the phase changes a system can experience The line that separates liquid and gas ends at the critical ii point The triple point is where solid, liquid, and gas phase regions all meet For water, this is 273.16 K This was actually used in the definition of the Kelvin scale Table 14.3 lists the melting and evaporation temperatures of some common substances Lecture 25 Purdue University, Physics 220 24
Phase Diagram H 2 O Lecture 25 Purdue University, Physics 220 25
Phase Diagram CO 2 Lecture 25 Purdue University, Physics 220 26
Ice ILQ Which can absorb more energy from your soda, a cooler filled with water at 0 C, or a cooler filled with ice at 0 C. A) Water B) About Same C) Ice Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid- gas). 0 o C Substance L f (J/kg) L v (J/kg) water 33.5 x 10 4 22.6 x 10 5 T ice temp rises ice changes to water (melts) Latent Heat water temp rises Q added to water Lecture 25 Purdue University, Physics 220 27
Exercise During a tough work out, your body sweats (and evaporates) 1 liter of water to keep cool (37 C). How much cold water would you need to drink (at 2 C) to achieve the same thermal cooling? (recall C 22 V = 4.2 J/g for water, L v =2.2x10 3 J/g) A) 0.15 liters B) 1.0 liters C) 15 liters D) 150 liters Q evaporative = L m = 2.2x10 3 kj/kg x 1kg Q c = c m Δt = 4.2kJ/kgK x 35K x m m = 22 2.2x10 3 / 147 = 15kg or 15 liters! Lecture 25 Purdue University, Physics 220 28
Boiling Point Going from Lafayette to Denver the temperature at which water boils: A) Increases B) Decreases C) Same Lecture 25 Purdue University, Physics 220 29
Boiling ILQ What happens to the boiling point when beaker is placed in ice-water? A) Increases B) Decreases C) Same Lecture 25 Purdue University, Physics 220 30
Cooling ILQ What happens to the pressure in the beaker when placed in ice-water? A) Increases B) Decreases C) Same PV = nrt Lecture 25 Purdue University, Physics 220 31
ILQ What will happen to the water in the container when I pour ice water over the container A) cool down B) Boil C) Both D) Neither Lecture 25 Purdue University, Physics 220 32
Exercise How much ice (at 0 C) do you need to add to 0.5 liters of a water at 25 C, to cool it down to 10 C? (L = 80 cal/g, c = 1 cal/g C) Q water = mc Δ T = (0.5 kg)(1 cal / gc)(15 C) = (7,500 calories) Q = ml + mc Δ T ice Qice m = L + c Δ T 7,500cal = = 80 cal / g + (1 cal / gc )(10) 83.3 grams Lecture 25 Purdue University, Physics 220 33
Exercise Ice cube trays are filled with 0.5 kg of water at 20 C and placed into the freezer. e How much energy e must be removed from the water to turn it into ice cubes at -5 C? (L = 80 cal/g, c water = 1 cal/g C, c ice = 0.5 cal/g C) Water going from 20 C to 0 C: Q = mc ΔT 1 water 1 = 500 1 ( 20) = 10000( cal) Water turning into ice at 0 C: Q2 = ml = 500 80 = 40000( cal ) Ice going from 0 C to -5 C: Q3 = mciceδt2 = 500 0.5 ( 5) = 1250( cal) Q= Q1+ Q2 + Q3 = 51250( cal ) Lecture 25 Purdue University, Physics 220 34
Summary of Concepts Heat is FLOW of energy Flow of energy may increase temperaturet Specific Heat ΔT = Q / (c m) Monatomic IDEAL Gas C V = 3/2 R Diatomic IDEAL Gas C V = 5/2 R V Latent Heat Heat associated with change in phase Lecture 25 Purdue University, Physics 220 35