Heat and Energy Lecturer: Professor Stephen T. Thornton

Heat and Energy

Lecturer: Professor Stephen T. Thornton

Reading Quiz A 5-kg cube of hot steel is put in thermal contact

with a 10-kg cube of cold steel. Which of the following statements is most valid:

A) Heat flows from the larger cube to the smaller one, because the larger cube has the most internal energy.

B) Heat flows from the warmer cube to the colder one until they have the same heat content.

C) Heat flows from the warmer cube to the colder one until they have the same temperature.

D) Heat transfers until both cubes have the same heat.

Reading Quiz

Answer: C

Heat content is a misnomer. Heat does not flow to make the internal energy the same, but rather to make the temperature the same.

Last Time

Kinetic energy of molecules Maxwell distribution Phase changes Vapor pressure and humidity Van de Waals Equation

Mean free pathDiffusion

Today

HeatInternal energySpecific heatLatent heatFirst Law of Thermodynamics

Heat and mechanical workAt one time it was thought that all substances contained a heat fluid or “caloric” that could flow from one substance to another.

The American royalist Benjamin Thompson (Count Rumford) finally figured out while boring cannons that friction caused heat flow, which is a form of energy.

Doing work causes heat flow,so they should be related.

Copyright © 2009 Pearson Education, Inc.

We often speak of heat as though it were a material that flows from one object to another; it is not. Rather, it is a form of energy flow.

Unit of heat: calorie (cal)

1 cal is the amount of heat necessary to raise the temperature of 1 g of water by 1 Celsius degree.

Don’t be fooled—the calories on our food labels are really kilocalories (kcal or Calories), the heat necessary to raise 1 kg of water by 1 Celsius degree.

Heat as Energy Transfer


Definition of heat:

Heat is energy transferred from one object to another because of a difference in temperature.

Remember that the temperature of a gas is a measure of the kinetic energy of its molecules.

Heat as Energy Transfer

Mechanical equivalent of heat

British physicist James Joule did experiment in mid-1800s to determine how heat is related to work and energy.

Now we know

Q = heat flow = energy transferred due to temperature differences.

1 cal = 4.186 J

1 Btu = 0.252 kcal = 1055 J

The Mechanical Equivalent of Heat


The sum total of all the energy of all the molecules in a substance is its internal (or thermal) energy.

Temperature: measures molecules’ average kinetic energy

Internal energy: total energy of all molecules

Heat: transfer of energy due to difference in temperature

Internal Energy


Internal energy of an ideal (monoatomic) gas (that is, its translational KE):

But since we know the average kinetic energy in terms of the temperature, we can write:

We often denote internal energy by U.

2int

1

2E N mv

æ ö÷ç= ÷ç ÷çè ø

int

3

2E NkT=


If the gas is molecular rather than atomic, rotational and vibrational kinetic energy need to be taken into account as well.

Internal Energy

What happens if we add pieces (same volume) of hot metal to Styrofoam cups with equal amounts of water at the same temperature? Aluminum and copper

Do experiment. Use thermometers and TV.

Drop two pieces of metal at 1000C into two cups containing room temperature water.

We find that the result depends on the metal (note final temperatures). Aluminum and copper are different.

Why?

We know that it takes 1 cal of heat energy to raise the temperature of water by 10C.

Heat capacityWe find that every substance has a specific property of heat capacity C:

Q is positive or negative depending on whether heat energy is added or removed from the object.

0 unit: J/K or J/ C

or

QC

T

Q C T

Specific heat• Heat capacity is not so useful because we must

specify type of substance and how much.

• We define a new quantity, called specific heat,

that depends on the particular substance.0

water

unit: J/(kg K) or J/(kg C)

For water: 4186 J/(kg K)

heat required to raise temperature

Qc

m Tc

Q mc T

T


The amount of heat required to change the temperature of a material is proportional to the mass, specific heat, and temperature change:

The specific heat, c, is characteristic of the material. Some values are listed at left.

Specific Heat

Q mc T= D

Two objects are made of the same material, but have different masses and temperatures. If the objects are brought into thermal contact, which one will have the greater temperature change?

A) the one with the higher initial temperature

B) the one with the lower initial temperature

C) the one with the greater mass

D) the one with the smaller mass

E) the one with the higher specific heat

Conceptual QuizConceptual Quiz

Two objects are made of the same material, but have different masses and temperatures. If the objects are brought into thermal contact, whichone will have the greater temperature change?

A) the one with the higher initial temperature

B) the one with the lower initial temperature

C) the one with the greater mass

D) the one with the smaller mass

E) the one with the higher specific heat

Because the objects are made of the same material, the only difference between them is their mass. Clearly, the object with less mass will change temperature more easily because not much material is there (compared to the more massive object).


Two different objects receive the same amount of heat. Which of the following choices is NOT a reason why the objects may have different temperature changes?

A) they have different initial temperatures

B) they have different masses

C) they have different specific heats


Two different objects receive the same amount of heat. Which of the following choices is NOT a reason why the objects may have different temperature changes?

A) they have different initial temperatures

B) they have different masses

C) they have different specific heats

Because QQ = = m cm c TT and the objects received the same amount

of heat, the only other factors are the masses and the specific heats. Although the initial temperature is certainly relevant for finding the final temperature, it does not have any effect on the temperature change T.


CalorimetryWe dropped 2 blocks of hot metal into Styrofoam cups of water. Calculate the final temperature.

Qmetal + Qwater = 0

Qm is the heat flow to metal (negative).

Qw is the heat flow to water (positive).

The metal loses heat energy to the water. There is a flow of heat energy from the metal to the water. The metal cools, and the water is hotter.

Sometimes I simply use Q(lost) = Q(gained)

( ) ( )

( ) ( )

( ) ( ) 0

is specific heat in J/kg K

m m m f im

w w w f iw

w w f iw m m f im

Q m c T T negative

Q m c T T positive

m c T T m c T T

c

Consider previous experimentQCu = mCucCuΔT = (0.0485 kg)(387 J/kg K) ΔT = 18.8 ΔT J

QAl = mAlcAlΔT = (0.0147 kg)(900 J/kg K) ΔT = 13.2 ΔT J

The Qmetal will be transferred to raise the water temperature. Which metal raised the temperature the most?

watermetal (lost) = (gained)Q Q

Latent heat L is the energy/kg needed to change the phase state of matter.

Latent heat of fusion LF is energy/kg needed

to melt a substance; solid goes to liquid.

Latent heat of vaporization LV is energy/kg

needed to go from liquid to gas.

Latent heat of sublimation LS is energy/kg

required to go from solid directly to gas.

Q mL


Energy is required for a material to change phase, even though its temperature is not changing.

Latent Heat

1 kg

Lf = 80 cal/g

Lv = 539 cal/g = 539 kcal/kg


The latent heat of vaporization is relevant for evaporation as well as boiling. The heat of vaporization of water rises slightly as the temperature decreases.

On a molecular level, the heat added during a change of state does not go to increasing the kinetic energy of individual molecules, but rather to breaking the close bonds between them so the next phase can occur.

Latent Heat

Will potatoes cook faster if the

water is boiling faster?

A) yes

B) no

C) depends on W


Will potatoes cook faster if the

water is boiling faster?

A) yes

B) no

C) depends on W

The water boils at 100 °C and remains at that temperature until all of the water has been changed into steam. Only then will the steam increase in temperature. Since the water stays at the same temperature, regardless of how fast it is boiling, the potatoes will not cook any faster.


Follow-up:Follow-up: How can you cook the potatoes faster?


You put 1 kg of ice at 0oC

together with 1 kg of water at

50oC. What is the final

temperature? LF = 80 cal/gcwater = 1 cal/g oC

A) 0oC

B) between 0oC and 50oC

C) 50oC

D) greater than 50oC

How much heat is needed to melt the ice?

QQ = = m Lm Lff = (1000= (1000gg) ) (80 cal/ (80 cal/gg) = 80,000 cal) = 80,000 cal

How much heat can the water deliver by cooling from 50oC to 0oC?

QQ = = ccwaterwater mmTT = (1 cal/ = (1 cal/gg ooC) C) (1000 (1000gg) ) (50 (50ooC) = 50,000 calC) = 50,000 cal

Thus, there is not enough heat available to melt all the ice!!


You put 1 kg of ice at 0oC

together with 1 kg of water at

50oC. What is the final

temperature? LF = 80 cal/gcwater = 1 cal/g oC

A) 0oC

B) between 0oC and 50oC

C) 50oC

D) greater than 50oC

Follow-up:Follow-up: How much more water at 50oC would you need?


Which will cause more severe burns

to your skin: 100 °C water or 100 °C

steam?

A) water

B) steam

C) both the same

D) it depends...

While the water is indeed hot, it releases only 1 cal/1 cal/gg of heat as it

cools. The steam, however, first has to undergo a phase phase

changechange into water and that process releases 540 cal/g540 cal/g, which is

a very large amount of heat. That immense release of heat is

what makes steam burns so dangerous.


Which will cause more severe burns

to your skin: 100 °C water or 100 °C

steam?

A) water

B) steam

C) both the same

D) it depends...

Consider a system:Automobile engineHuman bodySimple piston and cylinder

We want to consider what happens if we add heat to our system or take heat away.

Also let the system do work or have work done on it.

What happens to internal energy? The internal energy is the sum of all the kinetic and potential energies.

The Internal Energy of a System

If we add heat Q to a system having internal energy Ei, the new internal energy of the system is Ef = Ei + Q. E = Ef – Ei = Q

Ei Ef = Ei + Q

Work and Internal Energy

If the system does work W on the outside, then the system loses internal energy.

Ei – Ef = W E = Ef – Ei = -W

E

i

Ef = Ei -W

First Law of Thermodynamics(Conservation of Energy)

Let’s combine the last two equations:

E = Ef – Ei = Q

E = Ef – Ei = -W

Because both heat flow and work can occur, the change in internal energy of a system depends on both Q and W.

E Q W First law of thermodynamics

Signs of Q and W ***

Q positive System gains heat

Q negative System loses heat

W positive Work done by system

W negative Work done on system

The convention for W is opposite of that in chemistry.( )E Q W

The internal energy E depends on the state of the system (P, V, T, m, n). They are called state functions.

Heat flow Q and work W are not state functions. They depend on how the system is changed.

Documents

Heat and Energy Lecturer: Professor Stephen T. Thornton