Temperature, Heat, And Heat T: Ransfer

Chapter 1

Temperature, Heat, and Heat T ransfer Binyamin Mechanical Engineering Muhammadiyah University of Surakarta

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Temperature • Temperature is defined as a measure of how hot something is when we touch it. • Because related with the human’s feelings and s enses that they are not reliable and influenced b y psychological factors, temperature measureme nt should be defined exactly by certain scale. • Based on the zero law of the thermodynamics th at “if body A is in thermal equilibrium with body C , and body B is in thermal equilibrium with body C, then A is in thermal equilibrium with B, the the rmometer is made. 2

Temperature (con’t) • Two objects are in the thermal equilibrium me an that they are at the same temperature. • Suppose we want to measure the temperature of two beaker of liquid, A and B. We use a thermo meter as body C. Firstly we place it in contact wit h A and record a reading, say 22.5◦C. Then we place it in contact with B and again obtain the re ading 22.5◦C. Thus we know that A and B are at the same temperature and are in thermal equilib rium.

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Temperature Scale • To measure temperature we can use – Celsius – Kelvin (absolute temperature) – Fahrenheit

• The relation between Celsius, Kelvin, Fahrenheit; K = 273.15 + oC oF = 32 + 9/5 oC oC= 5/9 (oF-32)

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Thermal Expansion • Thermal expansion is phenomena occurred whe n the temperature of solid or liquid is change d. If at an initial temperature (To) an object has l ength Lo along some dimension, its length will c hange by an amount L = L-Lo, and From the ex perimental was be found that;

 L  Lo ( 1    T )  L  Lo  T

and

Where  Is the coefficient of linier expansion oC-1

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Thermal Expansion (con’t) • Area and volume also change with temper ature. • For area  Ao ( 1  2   T )  A  2 Ao  T A • For volume





 V  3 Vo  T  Vo  T

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Thermal Expansion (con’t)

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Example 1. Aluminum rivets (= 24x10-6 oC-1) used in airplane constr uction are made slightly larger than the holes into which t hey fit and then cooled in dry ice to -78 oC before being i nserted. When they then warm up to room temperature (23oC) they fit very tightly. If a rivet at -78oC is to be inse rted into a hole of diameter 3.20 mm, what should the diameter of the rivets be at 23oC.

2. A 100 cm3 beaker made of pyrex glass (=3.2x10-6C-1) i s filled to the brim with water at 12oC. What volume of wa ter will overflow when temperature is raised to 60oC. ( w ater=210x10-6C-1)

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Example (con’t) 3. A pair of eyeglass frames is made of epox y plastic. At room temperature (20.0°C), the frames have circular lens holes 2.20 c m in radius. To what temperature must t he frames be heated if lenses 2.21 cm i n radius are to be inserted in them? The a verage coefficient of linear expansion () f or epoxy is 1.30 x10-4 (°C)-1.

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HEAT AND THERMAL ENERGY

• Thermal Energy (=internal energy) of syste m is collective kinetic and potential ene rgy associated with the random motion of the atoms and molecules comprising the system. • Heat is the energy transferred between a system and its surroundings because of their temperature difference. 11

HEAT Substance Substance Internal energy Temperature

Internal energy Temperature 12

Heat and Thermal Energy (con’t)

• Heat flow is positive when energy flows into a system and negative when heat fl ows out.

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Unit of Heat • Heat is energy, so the unit of heat can be stated in joule, But for the thermal the unit of energy is calorie (cal). • 1 calorie is defined as the amount of energy transfer n ecessary to raise the temperature of 1 g of water from 14.5°C to 15.5°C. • From the mechanical equivalent of heat experiment condu cted by joule (see figure below) it is can be found that; 1 cal = 4.186 J • The other unit is Btu (British Thermal Unit), whereas 1 Btu = 252 cal = 1054 J

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The mechanical equivalent of heat Experiment

Energy measurement thermometer

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Heat Capacity and Latent Heat

• When heat is added to a substance the t emperature will rise or it changes from one phase (for example, solid, liquid or ga s) to another phase. • The resulting rise in temperature (T) dep ends on – The mass of substance – The heat added – The kinds of material 16

Heat Capacity and Latent Heat (con’t) • Property of material that influence the change of temperature when the heat added to the substan ce is a specific heat (c), where specific heat can be defined as the amount of heat required to r aise 1 kg of a substance by 1oC, while Heat c apacity (C) is the amount of heat required to rai se a substance by 1oC.

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Heat Capacity and Latent Heat (con’t) • The relationship between specific heat, amount of heat and changes of temperature can be writt en as;

Q  mc  T Where Q = heat (joule or calorie) m = mass c = specific heat (j/kg.oC or cal/g.oC T= changes of temperature

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Heat Capacity and Latent Heat (con’t) • Solid, liquid and gas (vapor) are called phase s of matter. To change it from some phase to th e other, energy must be added or removed. For example to transform substance from solid to liquid (melting process) or from liquid to gas (boiling process) energy must be supplied to the substance. Conversely, energy must be re moved to change from gas to liquid (condensing process) or from liquid to solid (freezing process ).

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Heat Capacity and Latent Heat (con’t) 





The energy that must be added (or removed) to cause the solid-liquid transition in 1kg of a given material is called t he latent heat of fusion (Lf). The energy that must be added (or removed) to cause the liquid-gas transition in 1kg of a given material is called the latent heat of vaporization (Lv). From the definition of latent heat, and again choosing he at as our energy transfer mechanism, we find that the en ergy required to change the phase of a given mass m of a pure substance is

Q mL

L is Lf or Lv 21

Heat removed Heat added

solid

gas Lv

Lf

liquid

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Heat Capacity and Latent Heat (con’t) • To explain completely, looking for example if -30 oC ice is heated (gained heat) continuously, the condition can be seen at graph below

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• Part A temperature increases, phase is still ice. • Part B, after temperature reaches 0oC (melting p oint of water), temperature still in 0oC and the ph ase will be changed from ice (solid) to water (liq uid). • Part C temperature increases from 0o to 100oC. • Part D after temperature reaches 100oC, (boiling point of water) temperature constant and phase will be changed to steam or vapor. • Part E, After all of water changed to vapor tempe rature will increase. 25

Hint Solution problem of heat capacity and heat lat

ent • If two substance or more are blended, then the s ubstance that has higher temperature will loo se of the energy and the other will gain the e nergy. • In a system, It is can be written as;

Qgained = -Qlost

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Problems Example 1. 80 grams of brass (c=0.092 cal/goC) at 292oC is adde d to 200 g of water (c=1 cal/goC) at 14oC in insulated container of negligible heat capacity. What is the final temperature of the system. 2. To 160 g of water at 10oC is added 200 g of iron (c=0. 11 cal/g.oC) at 80oC and 80 g of marble (c=0.21 cal/go C) at 20oC. What is the final temperature of the mixtur e. 3. Determine the amount of energy that must be lost by f reezer to make 1.5 kg of ice at -12oC from water at 20 oC. 27