Ying Yi PhD Chapter 12 Temperature and Heat 1 PHYS HCCS

Heat The process by which energy is exchanged between objects because of temperature differences is called heat Objects are in thermal contact if energy can be exchanged between them Thermal equilibrium exists when two objects in thermal contact with each other cease to exchange energy PHYS HCCS 2

Outline PHYS HCCS 3 Temperature scales Thermal expansion Temperature and phase change

Temperature Scales PHYS HCCS 4

Celsius Scale Temperature of an ice-water mixture is defined as 0º C This is the freezing point of water Temperature of a water-steam mixture is defined as 100º C This is the boiling point of water Distance between these points is divided into 100 segments or degrees PHYS HCCS 5

Kelvin Scale When the pressure of a gas goes to zero, its temperature is –273.15º C This temperature is called absolute zero This is the zero point of the Kelvin scale –273.15º C = 0 K To convert: T C = T – The size of the degree in the Kelvin scale is the same as the size of a Celsius degree PHYS HCCS 6

7 Some Kelvin Temperatures Some representative Kelvin temperatures Note, this scale is logarithmic Absolute zero has never been reached

Fahrenheit Scales Most common scale used in the US Temperature of the freezing point is 32º Temperature of the boiling point is 212º 180 divisions between the points PHYS HCCS 8

Thermometers Used to measure the temperature of an object or a system Make use of physical properties that change with temperature Many physical properties can be used Volume of a liquid Length of a solid Pressure of a gas held at constant volume Volume of a gas held at constant pressure Electric resistance of a conductor Color of a very hot object PHYS HCCS 9

Thermometers (Mercury) PHYS HCCS 10 A mercury thermometer is an example of a common thermometer The level of the mercury rises due to thermal expansion Temperature can be defined by the height of the mercury column

Comparing Temperature Scales PHYS HCCS 11

Converting Among Temperature Scales PHYS HCCS 12

Example 12.1 Fahrenheit to Celsius PHYS HCCS 13

Group Problem: Temperature scale PHYS HCCS 14 The temperature gradient between the skin and the air is regulated by cutaneous (skin) blood flow. If the cutaneous blood vessels are constricted, the skin temperature and the temperature of the environment will be about the same. When the vessels are dilated, more blood is brought to the surface. Suppose during dilation the skin warms from 72.0° F to 84.0°F. (a) convert these temperatures to Celsius and find the difference. (b) Convert the temperatures to Kelvin, again finding the difference.

Thermal Expansion due to Temperature Change PHYS HCCS 15

Thermal Expansion The thermal expansion of an object is a consequence of the change in the average separation between its constituent atoms or molecules At ordinary temperatures, molecules vibrate with a small amplitude As temperature increases, the amplitude increases This causes the overall object as a whole to expand PHYS HCCS 16

Examples PHYS HCCS 17

Linear Expansion PHYS HCCS 18

PHYS HCCS 19 Applications of Thermal Expansion – Bimetallic Strip Thermostats Use a bimetallic strip Two metals expand differently Since they have different coefficients of expansion

Example 12.3 Buckling of a sidewalk PHYS HCCS 20

Group Problem: Expansion of a railroad Track PHYS HCCS 21 (a) A steel railroad track has a length of m when the temperature is 0°C. What is its length on a hot day when the temperature is 40.0°C?

Volume Expansion PHYS HCCS 22

More Applications of Thermal Expansion Pyrex Glass Thermal stresses are smaller than for ordinary glass Sea levels Warming the oceans will increase the volume of the oceans PHYS HCCS 23

Example: Global warming PHYS HCCS 24

PHYS HCCS 25 Unusual Behavior of Water As the temperature of water increases from 0ºC to 4 ºC, it contracts and its density increases Above 4 ºC, water exhibits the expected expansion with increasing temperature Maximum density of water is 1000 kg/m 3 at 4 ºC

Temperature and Phase Change PHYS HCCS 26

Energy Transfer When two objects of different temperatures are placed in thermal contact, the temperature of the warmer decreases and the temperature of the cooler increases The energy exchange ceases when the objects reach thermal equilibrium The concept of energy was broadened from just mechanical to include internal PHYS HCCS 27

Heat Heat is the transfer of energy between a system and its environment because of a temperature difference between them The symbol Q is used to represent the amount of energy transferred by heat between a system and its environment PHYS HCCS 28

Units of Heat SI unit: joule (J) Other units: calorie, Calorie 1 cal = J PHYS HCCS 29

Examples PHYS HCCS 30

James Prescott Joule 1818 – 1889 British physicist Conservation of Energy Relationship between heat and other forms of energy transfer PHYS HCCS 31

Heat and Specific Heat Q = m c Δ T Δ T is always the final temperature minus the initial temperature When the temperature increases, Δ T and Δ Q are considered to be positive and energy flows into the system When the temperature decreases, Δ T and Δ Q are considered to be negative and energy flows out of the system PHYS HCCS 32

Specific Heat Every substance requires a unique amount of energy per unit mass to change the temperature of that substance by 1° C The specific heat, c, of a substance is a measure of this amount SI units: J / kg °C Historical units: cal / g °C PHYS HCCS 33

Specific Heats Table PHYS HCCS 34

A Consequence of Different Specific Heats Water has a high specific heat compared to land On a hot day, the air above the land warms faster The warmer air flows upward and cooler air moves toward the beach PHYS HCCS 35

Example 12.9 A hot Jogger PHYS HCCS 36

Group Problem: heating water PHYS HCCS 37

Energy transfer in a system In some cases it may be difficult to determine which materials gain heat and which materials lose heat You can start with  Q = 0 Each Q = m c  T Use T f – T i You don’t have to determine before using the equation which materials will gain or lose heat PHYS HCCS 38

Problem Solving Hint It is important to organize the information in a problem A table will be helpful Headings can be Q material m c T f T i PHYS HCCS 39

Example Measuring specific heat PHYS HCCS 40

Group Problem: Calculate an Equilibrium Temperature PHYS HCCS 41 Suppose kg of water initially at 40.0 °C is poured into a kg glass beaker having a temperature of 25.0°C. A kg block of aluminum at 37.0°C is placed in the water and the system insulated. Calculate the final equilibrium temperature of the system.

Phase Change PHYS HCCS 42 Note that: Phases changes involve a change in the internal energy, but no change in temperature

Latent Heat During a phase change, the amount of heat is given as Q = ±m L L is the latent heat of the substance Latent means hidden L depends on the substance and the nature of the phase change Choose a positive sign if you are adding energy to the system and a negative sign if energy is being removed from the system PHYS HCCS 43

Latent Heat, cont. SI units of latent heat are J / kg Latent heat of fusion, L f, is used for melting or freezing Latent heat of vaporization, L v, is used for boiling or condensing Table 12.3 gives the latent heats for various substances PHYS HCCS 44

Example ice-cold Lemonade PHYS HCCS 45

Graph of Ice to Steam PHYS HCCS 46

Warming Ice Start with one gram of ice at –30.0º C During A, the temperature of the ice changes from –30.0º C to 0º C Use Q = m c Δ T Will add 62.7 J of energy PHYS HCCS 47

Melting Ice Once at 0º C, the phase change (melting) starts The temperature stays the same although energy is still being added Use Q = m L f Needs 333 J of energy PHYS HCCS 48

Warming Water Between 0º C and 100º C, the material is liquid and no phase changes take place Energy added increases the temperature Use Q = m c Δ T 419 J of energy are added PHYS HCCS 49

Boiling Water At 100º C, a phase change occurs (boiling) Temperature does not change Use Q = m Lv J of energy are needed PHYS HCCS 50

Heating Steam After all the water is converted to steam, the steam will heat up No phase change occurs The added energy goes to increasing the temperature Use Q = m c Δ T To raise the temperature of the steam to 120°, 40.2 J of energy are needed PHYS HCCS 51

Problem Solving Strategies Make a table A column for each quantity A row for each phase and/or phase change Use a final column for the combination of quantities Use consistent units PHYS HCCS 52

Problem Solving Strategies, cont Apply Conservation of Energy Transfers in energy are given as Q=mc Δ T for processes with no phase changes Use Q = m L f or Q = m L v if there is a phase change Start with  Q = 0 Or Q cold = - Q hot, but be careful of sign Δ T is T f – T i Solve for the unknown PHYS HCCS 53

Group Problem: Ice Water PHYS HCCS 54 At a party, 6.00 kg of ice at °C is added to a cooler holding 30 liters of water at 20.0°C. What is the temperature of the water when it comes to equilibrium?

Homework PHYS HCCS 55 3, 11, 15, 31, 47, 51, 57, 61, 62