Chapter 11 Thermal Physics Temperature A quantitative measure

Chapter 11: Thermal Physics Temperature: A quantitative measure of “hot” or “cold” Operational definition: Temperature is what is measured by a thermometer. mercury thermometer constant volume gas thermometer bimetallic strip All involve measurable physical changes in response to temperature changes. Temperature Scales water freezes water boils Fahrenheit 32º 212º Celsius 0º 100º TF = 9/5 TC + 32 Examples: What Fahrenheit temperature corresponds to 37. 0 ºC? to 20. 0 ºC? What Celsius temperature corresponds to 86 ºF? Phys 250 Ch 10 p 1

Gas thermometer and absolute temperature scales Constant volume gas thermometer pressure changes indicate temperature changes At low densities Dp µDT All gases have same x-intercept p = 0 at TC = -273ºC TF = -460ºF Absolute temperature scales: T = 0 when p = 0 Kelvin TK = TC + 273 Rankine TR = TF + 460 Phys 250 Ch 10 p 2 p TC = -273ºC T (Celsius) TC = 0ºC

Thermal Expansion A change in temperature causes a change in length in a solid object. Usually, change in length DL is proportional to change in temperature, DT is proportional to original length, L 0 depends upon type of material L 0 DL a = Coefficient of Linear Expansion (sometime a) Determine a experimentally: Phys 250 Ch 10 p 3

Example: The center span of the Verrazano-Narrows Bridge is 1300 m long. Assuming the bridge is made of steel, how much expansion will there be for a temperature range of 120ºC? Phys 250 Ch 10 p 4

Example: A copper hot-water pipe is 10. 0 m long when installed on a day when the temperature is 10ºC. How long is the pipe when it carries hot water at 60ºC if the pipe is free to expand? Phys 250 Ch 10 p 5

Volume expansion (of solids and liquids) linear expansion in 3 -D! A change in temperature causes a change in volume. The change in volume DV is proportional to change in temperature, DT is proportional to original length, V 0 depends upon type of material b = Coefficient of volume expansion for solids, b= 3 a How are voids (holes) in materials affected by changing temperatures? Phys 250 Ch 10 p 6

Voids in materials expand contract as if they were made of the material. Example: How much water overflows from a 1 liter glass beaker filled to the brim with water at 20°C when beaker and contents are both heated to 95° C? Use average value of b = 525 E-6/ºC Phys 250 Ch 10 p 7

What is heat? One thing which is transferred between two systems initially at different temperatures as they come to thermal equilibrium. Heat is energy which is transferred solely because of temperature differences. Heat addition to a system can cause temperature changes. “Mechanical Equivalent” of Heat: 1 calorie = 4. 187 joules Heat Units, defined in terms of the properties of water calorie: the energy required to raise the temperature of 1 gram of water by 1 ºC (4. 187 J) kilocalorie: a. k. a. Calorie a. k. a. dietetic calorie = 1000 calories (4187 J) British Thermal Unit: the energy required to raise the temperature of 1 pound of water by 1 ºF (1060 J) Example: A candy bar has 200 dietetic Calories. How many time must a 10 kg weight be lifted through a height of 2 m to work off the candy bar if the human body is 10% efficient at converting calories to mechanical energy? Phys 250 Ch 10 p 8

Calorimetry For a sample of a substance that does not undergo a change of state: Heat added: Q is proportional to DT = Tf- Ti , the change in temperature m, the mass of the sample Q = mc DT c is the material’s specific heat In a closed system (hot object interacts with cool object) heat gained by cool object(+) + heat lost by hot object(-) =0 Phys 250 Ch 10 p 9

Example: A Styrofoam cup of negligible heat capacity contains 150 g of water at 10ºC. If you add 100 g of water at 85ºC, what is the final temperature of the mixture? Phys 250 Ch 10 p 10

Example: A 74 g metal block is heated to 90ºC. It is then submerged in 300 g of water at 10ºC. The final temperature is 14ºC. What is the specific heat of the material? Phys 250 Ch 10 p 11

Phase Changes Phase of Matter: solid, liquid, gas etc. Phase Change (Phase Transition) solid -> liquid (melting), liquid -> gas (boiling) heat added (or removed) without a change in temperature (reversible process) Two states of matter coexist (in equilibrium) only at the transition temperature amount of heat proportional to mass of substance Q = m. L L is the Latent heat Water: Latent heat of fusion is the energy cost to convert a unit mass of ice at the melting temperature to a unit mass of water at the melting temperature. Lf = 80 kcal/kg = 334 k. J/kg Latent heat of vaporization is the energy cost to convert a unit mass of water at the boiling temperature to a unit mass of steam at the boiling temperature. Lv = 540 kcal/kg = 2260 k. J/kg T steam water-steam ice-water Phys 250 Ch 10 p 12 ice water Q

Water: Latent heat of fusion is the energy cost to convert a unit mass of ice at the melting temperature to a unit mass of water at the melting temperature. Lf = 80 kcal/kg = 334 k. J/kg Latent heat of vaporization is the energy cost to convert a unit mass of water at the boiling temperature to a unit mass of steam at the boiling temperature. Lf = 540 kcal/kg = 2260 k. J/kg T steam water-steam ice-water ice Phys 250 Ch 10 p 13 water Q

Example: A 105 g copper calorimeter contains 307 g of water at 23ºC. If 52 g of ice at 0ºC is added to the calorimeter, what is the final temperature of the system? Example: A 105 g copper calorimeter contains 307 g of water at 23ºC. If 95 g of ice at 0ºC is added to the calorimeter, what is the final temperature of the system? Phys 250 Ch 10 p 14

Mechanisms of Heat Transfer Conduction Convection (Natural vs Forced) Radiation (Electromagnetic Waves) Conduction: No bulk motion of matter Microscopic transfer of kinetic energy to adjacent regions Because KE of electrons in a conductor “easily” transported from one region to another, good electrical conductors are generally good thermal conductors Rate of heat flow: T 2 T 1 H Phys 250 Ch 10 p 15 A

Example: A Styrofoam cooler has a surface area of 0. 50 m 2 and an average thickness of 2. 0 cm. How long will it take for 1. 5 kg of ice to melt if the outside temperature is 30ºC? use K=0. 030 W/(m ºC) Phys 250 Ch 10 p 16

Convection Bulk motion of fluid (forced or natural) chief mechanism of heat lost under most situations COMPLEX!!! Depends upon fluid and geometry h = skin coefficient; depends upon temperatures, fluid, geometry, etc. Radiation (electromagnetic waves) = “Blackbody” Radiation Stephan- Boltsmann Law: Phys 250 Ch 10 p 17

Radiation (electromagnetic waves) =“Blackbody” Radiation Stephan- Boltsmann Law: I l Phys 250 Ch 10 p 18

Example: A patient waiting to be seen by his physician is asked to remove all his clothes in a room that is at 16ºC. Calculate the rate of heat loss by radiation given that the patient has a temperature of 34ºC and his surface area is 1. 6 m 2. Assume an emissivity of 0. 80. Phys 250 Ch 10 p 19