Heat and Thermodynamics

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H t d Th d iHeat and Thermodynamics

Physics Rapid Learning Series

Rapid Learning Centerwww.RapidLearningCenter.com/© Rapid Learning Inc. All rights reserved.

Wayne Huang, Ph.D.Keith Duda, M.Ed.

Peddi Prasad, Ph.D.Gary Zhou, Ph.D.

Michelle Wedemeyer, Ph.D.Sarah Hedges, Ph.D.



Learning Objectives

Temperature: Understand the definition of temperature.

By completing this tutorial, you will learn:

Energy in Thermal Processes. Understand the relationship between heat and internal energy.Thermal Processes in your world. Global warming and greenhouse gasses.

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Laws of Thermodynamics. Apply the laws of thermodynamics to real life problems such as engines and human metabolism.

Concept MapPhysics

Studies

Previous content

New content

Thermodynamics

The field of

Matter and EnergyMatter and Energy

Heat Energy

One type of energy is

2nd Law1st LawExpansionThermal

Expansion

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Heated objects Heated objects expand

Energy is

destroyed

Energy is neither created nor

destroyed

Entropy

increases

Entropy always

increases

States thatStates that States that



ThermodynamicsThermodynamics and Thermal Expansion

Thermometers and Temperature Scales. Thermal expansion of Solids and Liquids

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Thermal expansion of Solids and Liquids

Thermodynamics and Temperature

How does temperature affect materials and how is this used to measure temperature?

Linear expansion

Volume expansion

The physics of thermostats

The physics of

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thermometers



Definition - Thermodynamics

Thermodynamics - The branch of physics that deals with conversionsphysics that deals with conversions between heat energy and other forms of energy.

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Thermal ExpansionAs solids and liquids are heated, they expand because their molecules gain kinetic energy and move around more.

Expansions of solids can be predicted using the linear expansion equation.

Expansions of liquids can be predicted using the volume expansion equation.

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p q

The ticking noises heard after a hot car is shut down are due the shape changes of engine parts as they cool.



Linear Expansion Equation

The linear expansion equation is of the form:

Where:

L = length of objectT = temperature

∆TαL∆L ××=

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pα = coefficient of linear expansion [units = per degree]∆ = Greek letter “delta”, change in.

Volume Expansion Equation

Similarly, the volume expansion equation is of the form:

∆TβV∆V ××=

Where:

V = volume of objectT = temperature

∆TβV∆V ××=

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ß = coefficient of volume expansion [units = per degree]∆ = Greek letter “delta”, change in.



Expansion Coefficients

Note the units of the expansion coefficients:

1∆Lα ×= 1∆Vβ ×=

The linear and volume expansion coefficients are

Thus, length and volume cancel. Both expansion coefficients have units of “per degree”

∆TLα ×

∆TVβ ×

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The linear and volume expansion coefficients are related to each other by the following relationship:

Typical values for expansion coefficients may be found in your physics textbook.

α3β ×=

Sample Problem: Thermal ExpansionQuestion: How much will the volume of a 2 cm3 aluminum cube change if the temperature changes from 12°C to 32°C? The linear expansion coefficient, α, of aluminum is 23x10-6/°C.

S l tiSolution:

Step 1: Use the volume expansion equation.∆V = Vß * ∆T

Step 2: Calculate ∆T.∆T = Tfinal –Tinitial = 32°C – 12°C = 20°C

St 3 C l l t ß

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Step 3: Calculate ß.ß = 3α = 3 * 23 x10-6/°C = 69 x 10-6/°C

Step 4: Plug in the values.∆V = Vß * ∆T = (2cm3) * (69x10-6/°C) * (20°C)

Answer: ∆V = 2.76x10-3 cm3



Note - Units and Temperature Change

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Thermostats - 1Thermostats are designed to measure temperature by applying the principle of linear expansion.

A thermostat uses two fused strips of metal, each with a different linear expansion coefficient. As the strip heats up one strip lengthens faster so the strips

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bend away from the longer strip.Typically the bent strips will make contact with a circuit.



Thermostats - 2Imagine a thermostat made up of two metal strips as shown below. The yellow strip has a larger linear expansion coefficient.

Heat

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Heat

The strip bends towards the side with the lower linear expansion coefficient.

ThermometersThermometers are designed to measure temperature by applying the principle of thermal expansion.Most home thermometers use mercury or alcohol inside a narrow glass tube. As the temperature rises, both the glass and liquid expand.The liquid has a higher volume

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The liquid has a higher volume expansion coefficient than the glass tube so it rises within the tube to tell you the temperature.



Thermal Expansion: Stop-And-Think

Question: Why would engineers need to take thermal expansion into account in the design of bridges?

On hot days, the metal supports of a bridge will expand and buckle if the bridge is not designed to expand. Similarly, the bridge will crack as the supports shrink on a cold day.

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Energy in Thermal Processes

Heat and Internal EnergySpecific Heat

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Specific HeatCalorimetryLatent Heat and Phase ChangeEnergy TransferGlobal Warming and Greenhouse Gasses



System vs. Surroundings

Calculations of heat and internal energy are based on the definition of a system and its surroundings.

System - The system refers to the object being studied.

Surroundings -

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gEverything not included in the system.

Example - System v. Surroundings

Example: a beaker

The system refers to the contents of the beaker.

Th di f

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The surroundings refer to everything else.



Heat and Internal Energy Equation

Internal energy of a system is defined as: 1) The ability to do work on an object.2) The ability to transfer heat to an object.

U = q + w

Heat

Heat energy of the system

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q

Internal Energy Work

System internal energy

Work done on the system or energy available for the

system to do work.

Definition - Energy Units

Calorie (cal) - Heat is measured in calories. A calorie is the amount of heat required to heat 1 gram of water 1°C.

Joule (J) - Energy is measured in Joules. One calorie (cal) is equal to 4 18J

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4.18J.

4.18 J = 1 cal



Definition - State Function

State Function - n. A state function is a quantity of the object that isa quantity of the object that is dependent on the current state. A state function is independent of the path taken to reach the current state.

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Temperature, kinetic energy, and potential energy are all state functions.

Temperature is a State Function

Temperature is an example of a state function. Your coffee can be 40°C whether you heated it in the microwave or on the stove.

24/6740°C



Note: the Food Calorie

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Definition - Specific Heat

Specific Heat (CP) - n. Specific heat p ( P) pis a material property that defines the quantity of heat, q, required to raise 1g of a specific material 1°C.

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units of cp = [cal/gram*K]



Specific Heat Equation

T T

The specific heat may be used as follows:

Q = CPm * ∆T

Specific Heat Change in Temperature

Tfinal - Tinitial(K) or (°C)

Proportionality ConstantJ/g*K or cal/g*K

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P

HeatTotal Heat Energy

(J)

MassMass of Object

(g)

Interpretation of Specific HeatWhat are the practical implications of specific heat?

High Specific Heat Low Specific Heat

Large amount of energy to change temperature

Small amount of energy can change temperature

Heats up slowly

Cools down slowly

Small temperature changes with condition changes

e g Water Cast iron

Heats up quickly

Cools down quickly

Quickly readjusts to new conditions

e g Air aluminum foil

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e.g. Water, Cast-iron e.g. Air, aluminum foil

A pool takes a long time to warm up and remains fairly warm over night.The air warms quickly on a sunny day, but cools quickly at night

A cast-iron pan stays hot for a long time after removing from oven.Aluminum foil can be grabbed by your hand from a hot oven because it cools so quickly



Specific Heat and Heat Capacity

Thus, if the specific heat and the mass of any object are known, then the amount of heat need to raise the temperature by any given amount may be calculated.

The heat capacity C of an object may be determined from its specific heat CP and its mass m as follows:

CmC ×

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C = heat capacityCP = specific heat

m = mass of object

pCmC ×=

Definition - Heat Capacity

Heat Capacity (C) - The amount of heat Q required to raise the temperature of an object by ∆T is given by:

Q = C * ∆T

Heat Capacity

Proportionality Constant

J/K or cal/K

object by ∆T is given by:

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Q = C * ∆T

Heat Change in TemperatureTfinal - Tinitial(K) or (°C)

Total Heat Energy(J)



Definition - Enthalpy (H)

Enthalpy of Reaction (H) - The enthalpy of a reaction is the heat energy (J) gained or lost during a reaction. Enthalpy is a state function.during a reaction. Enthalpy is a state function.

ReactionBonds of reactants broken. Bonds of products formed.

Bonds of reactants have hi h th

Bonds of products have higher energy than

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higher energy than bonds of products.

higher energy than bonds of reactants.

Exothermic Endothermic

Heat given off by system

Heat absorbed by

system

Endothermic vs. Exothermic

Exothermic - If the system looses net heat during a reaction, the reaction is g ,exothermic.

Endothermic - If the system gains net

∆Hsystem = Hfinal – Hinitial < 0

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y gheat energy during a reaction, the reaction is endothermic.

∆Hsystem = Hfinal – Hinitial > 0



Definition - Calorimetry

Calorimetry. n. Calorimetry is aCalorimetry is a laboratory technique used to determine the amount of heat Q taken up or given off

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by a reaction.

Procedure - Calorimetry

A small beaker is immersed in an insulated 1

How to determine the heat of a reaction using calorimetry.

beaker filled with a known amount of water.

The initial temperature of the water is noted.A known amount of the reactants are placed in the small reaction beaker.The temperature of the water is recorded at

1

2

3

4

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regular intervals as the reaction proceeds.

The change is temperature is plotted versus time.

4

5

6The heat given off by the reaction is calculated from the total change in temperature of the water.



Example - Calorimetry

(1) Large, insulated beaker

(2) Water initial(2) Water, initial temperature Tinitial

(3) Reaction beaker

(4) Initiate reaction

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(5) Flow of heat energy to water

(6) Measure final water temperature, Tfinal

(7) Calculate ∆H from ∆Twater and the specific heat of water, CP.

Endothermic vs. Exothermic Reactions

Endothermic Exothermic

Heat moves from Heat moves from system surroundings to system

Internal energy of system increases

KEAVE of system molecules increases

Internal energy of system decreases

KEAVE of the system decreases

to surroundings.

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Temperature of the system increases

Bonds of reaction products have greater energy than bonds of reactants

Temperature of the system decreases.

Chemical bonds of reactants have greater energy than bonds of products.



Stop and Think- Calorimetry

Question: If the temperature of the water in a l i t i t i i th ticalorimetry experiment rises, is the reaction

endothermic or exothermic?

Answer: The reaction is exothermic because heat energy is moving from the system (the reaction) to

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energy is moving from the system (the reaction) to the surroundings (the water).

Latent Heat and Phase Change

A rise in temperatureInternal energy increases

When a solid is heated it undergoes the following:

Internal energy increases

Molecules oscillate more rapidly

A phase change from solid to liquidMolecules oscillate so rapidly they loose their crystalline form

There is no increase in temperature during the transition

Another rise in temperature

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Another rise in temperature

A phase change from liquid to gasMolecules oscillate so rapidly they escape the intermolecular forces that bind them together and enter the gas phase

There is no increase in temperature during the transition.



Heats of Fusion and Vaporization

The amount of heat Qfus needed to melt m grams of a substance is given by the following equation:

fusfus Lm∆Q ×=

Qfus = heat energy = [calories]m = mass = [grams]Lfus = Heat of Fusion = [calories/gram]

The amount of heat Qvap needed to vaporize m grams of a substance is given by the following equation:

fusfus Lm∆Q ×

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Qvap = heat = [calories]m = mass = [grams]Lvap = Heat of Vaporization = [calories/gram]

of a substance is given by the following equation:

vapvap Lm∆Q ×=

Latent Heat and Phase Change

Gas

Tem

pera

ture

of

Subs

tanc

e

Phase

Liquid Phase

Solid

Tboil

Tmelt

40/67Increase in Heat Energy, ∆Q

Solid Phase

QmeltQboil



Example - Heats of TransformationQuestion: How much heat energy is required for 10 grams of ice at 0°C to transition to liquid? To evaporate? The heat of fusion for water is 333 KJ/kg. The heat of vaporization is 2256 KJ/kg.Solution:Solution:

1) Calculate the heat energy required to melt 10 grams (0.01Kg) of ice.Qfus = Lfus * m = 333 KJ/kg * 0.01 Kg = 3.33 KJ

2) Calculate the heat energy needed to raised the temperature of the water from 0°C to 100°C.

Q = 0.00418 KJ/g*°C * 10.0 g * (100-0)°C = 4.18 kJ

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3) Calculate the heat energy required to vaporize 10g of water.Qvap = Lvap * m = 2256 KJ/kg * 0.01Kg = 22.56 KJ

4) The total heat required is the sum of 1-3.Qtot = 3.33 KJ + 4.18 KJ + 22.56 KJ = 30.07 KJ

Answer: Qtot = 30.07 KJ

Stop-and-think- Sweating

Question: Why is sweating an effective cooling mechanism?

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Answer: As sweat evaporates from your skin it transitions from the liquid to the gas phase. This phase transition requires a transfer of heat energy from the skin to the liquid, cooling the skin.



Global Warming & Greenhouse Gases1) Heat energy radiates from the

sun to the earth

2) Some of the heat energy is reflected off greenhouse gasesreflected off greenhouse gases in the earth’s atmosphere.

3) Some of the heat energy is reflected of the earth’s surface.

4) Some of the energy reflected off the surface is trapped by greenhouse gases in the

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atmosphere.

5) As the concentration of greenhouse gases is increased due to emissions from cars and factories, the temperature of the earth rises.

The Laws of Thermodynamics

The Zeroth Law of ThermodynamicsWork in Thermodynamic Processes

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Work in Thermodynamic ProcessesThe First Law of ThermodynamicsHeat, Engines, and the Second Law of

ThermodynamicsEntropyHuman Metabolism



Heat Energy and the Laws of Thermodynamics

The Zeroth Law of Thermodynamics states that objects in thermal

ilib i t th

The laws of thermodynamics govern energy exchanges:

equilibrium are at the same temperature.

The internal energy of a system is the sum of the heat energy of the system and the work done on or by the system.

The 1st Law of Thermodynamics states that energy can change state but cannot

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gy gbe created or destroyed.

The 2nd Law of Thermodynamics states that the total entropy, or disorder, of the universe can increase or stay the same but never decrease. The universe tends towards disorder.

Definition: Thermal Equilibrium

Thermal Equilibrium - Two objects are thermal equilibrium are at the same qtemperature. That is, when put in contact they remain at the same temperature and no longer exchange net heat energy.

A and B areIf A is placed in The temperature

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A and B are said to be in

thermal equilibrium.

pcontact with B,

they both remain at 10C°.

The temperature of A is 10C° and the temperature

of B is 10C°

Note that if objects are in thermal equilibrium, their molecules also have the same average kinetic energy



Zeroth Law of ThermodynamicsZeroth Law - If object A is in thermal equilibrium with object B and object C, then objects B and C are also in thermalthen objects B and C are also in thermal equilibrium.

A10 degrees

Celsius

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B C10 degrees

Celsius10 degrees

Celsius

Note that if B and C are in thermal equilibrium with A, then they must also be at 10 degrees Celsius.

Work in Thermodynamics

As mentioned before:

U = q +U = q + w

U = system internal energyq = heat energyw = work done on or by the system

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Pressure-Volume Work

For constant pressure:

∆W = -P * ∆V

∆W = work done on or by the systemP = pressure∆V = volume change of the system

One common type of application of this equation is in calculating pressure-volume work done by

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engines.

Applied Pressure-Volume Work

If the system expands, work is done by the system on the surroundings. The internal energy of the systeminternal energy of the system decreases.

If the system contracts, work is done

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by the surroundings on the system. The internal energy of the system increases.



The First Law of Thermodynamics

Energy in a reaction may be changed from one form to another but it is neither

t d d t d ti fcreated nor destroyed – conservation of energy.

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Application of The 1st Law

This implies that:

Q Q

∆U = ∆q + ∆w

Change in Heat Energy

W k d t b

Qinitial -Qfinal

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Change in System Internal Energy

Work done to or by the system

Ufinal - Uinitial Win -Wout



Work and the 1st Law

There are 4 special applications of the 1st Law:

1) Adiabatic: Q = 0, ∆U = -W

2) Constant-volume: W = 0, ∆U = Q

3) Cyclical: ∆U = 0, Q = -W

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4) Free expansion processes: ∆U = Q = W

Adiabatic WorkAn example of adiabatic work is a closed system with a piston. If pressure is applied rapidly to depress the piston, the volume of the system will decrease. Work W is done on the system by the surroundings, but there is

∆V ≥ 0 Q = 0, ∆U = -W = -P*∆V

is done on the system by the surroundings, but there is no change in heat Q so the change in internal energy ∆U is equal to –W.

W

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W

Vinitial Vfinal



Constant-Volume WorkAn example of constant-volume work is heating a sealed cylinder. There is no volume change so the change in internal energy is equal to the change in heat energyenergy.

Tinitial Tfinal

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∆V = 0 so W = 0∆T ≥ 0 so Q ≥ 0

∆U = Q

Cyclical Work and EnginesIn an engine, heat is used to increase pressure leading to an increase in volume. The change in volume does work on the surroundings. The work energy is transferred back from the surroundings to compress the cylinder back to its original size and the cycle repeatsand the cycle repeats.

∆U = 0 Q W

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Q = -W



Free Expansion WorkConnecting a pressurized system to a vacuum is an example of free-expansion work. The gas from the pressurized system will immediately and irreversibly expand to fill the vacuum The process occurs rapidlyexpand to fill the vacuum. The process occurs rapidly, but unlike adiabatic work the process is irreversible.

∆U = Q = W = 0

Heating an open beaker may be considered free-i k Th t th t t f th

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expansion work. The system, the contents of the beaker, are open to the surroundings so there can be no volume changes or heat exchanges.

Energy Calculations: Example

Question: If the volume of a sealed balloon increases from 10mL to 100mL when heated and then shrinks back to 10mL as it cools, what

f tapplication of the 1st Law is this?

Constant-volume

Adiabatic

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Cyclical



Energy Calculations: Answer

Question: If the volume of a sealed balloon increases from 10mL to 100mL when heated and then shrinks back to 10mL as it cools, what

f tapplication of the 1st Law is this?

Constant-volume

Adiabatic

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Cyclical

Definition - Entropy

Entropy (S) - n. Entropy is a measure of the disorder of a system or its surroundings.surroundings.

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A landfill possesses lots of entropy!



The 2nd Law of ThermodynamicsThe 2nd Law of Thermodynamics states that the total entropy of the universe can never decrease, it can only increase or stay the same.

∆Stotal ≥ 0

Note that the entropy of the system may decrease, so long as the entropy of the s rro ndings increases b an eq al or greater

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surroundings increases by an equal or greater amount.

Thus, ∆Ssys + ∆Ssur ≥ 0

Relative Entropies

Low entropy states are more organized than high entropy states.

Lower Entropy Higher Entropy

Your clean bedroom Your room after finals

Solids Liquids

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Liquids

Salt tablets in water

Gases

Dissolved salt in water



Definition - Engine EfficiencyIn a real combustion engine such as your car, some of the work energy is lost to the surroundings as heat rather than transferred to pressure-volume work which moves a piston.

The efficiency of an engine is the ratio of the heat energy put in (for example by combustion) to the work output by the engine (such as movement of the wheels of a car).

ε = Wout / Qin

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If the efficiency of an engine is 0.7, the 30% of the heat from combustion is lost as heat to the surroundings. In the real world, this would be a very efficient engine!!!

Entropy and Human Metabolism

Question: Metabolic processes in the body, such as the building of proteins and DNA, lead to increased order. How does this not violate the 2nd Law?

Answer: Although the building of structural proteins in the body lead to increased order in the system, which is the body, they lead to increased disorder in the surroundings through loss of heat.

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surroundings through loss of heat. Metabolic processes are usually linked to a catabolic process such as the combustion of glucose or the flow of ions down a concentration gradient.



Entropy: Stop-and-Think QuestionQuestion: When an ice cube melts, does system entropy increase, decrease, or remain the same?

Pick the best answerPick the best answer.A. Remain the same because there is no reaction, only a state change.

B. Increase because the molecules are changing

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g gfrom an ordered crystalline state to a disordered liquid state.C. Decrease because heat is absorbed to melt the ice.

Entropy: Stop-and-Think AnswerQuestion: When an ice cube melts, does system entropy increase, decrease, or remain the same?

Pick the best answerPick the best answer.A. Remains the same because there is no reaction, only a state change.

B. Increases because the molecules are changing

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g gfrom an ordered crystalline state to a disordered liquid state.C. Decreases because heat is absorbed to melt the ice.



Entropy is a Entropy is a

Expansion coefficients

measure how

Expansion coefficients

measure how

The 2nd Law states that net

entrop can

The 2nd Law states that net

entrop can

Learning Summary

Heat energy mayHeat energy may

measure of disorder.

measure of disorder.

measure how much objects expand when

heated.

measure how much objects expand when

heated.

entropy can never

decrease.

entropy can never

decrease.

The 1st LawThe 1st Law

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Heat energy may be gained or lost

to the surroundings during work.

Heat energy may be gained or lost

to the surroundings during work.

The 1 Law states that

energy is never created or destroyed.

The 1 Law states that

energy is never created or destroyed.

CongratulationsY h f ll l t dYou have successfully completed

the tutorial

Heat and Thermodynamics

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