Heat, Temperature, and Internal Energy

StarterIf a Fahrenheit thermometer registers a 10 degree temperature increase in air temperature, what increase would a Celsius thermometer register?

Note: DFo/DCo = 180/100

Why?

10/DC = 9/5 DC = 10(5/9) = 5.55

Internal Energy E• The total kinetic energy of all the molecules in the

substance.• The units are Joules.

Example: A gas sample consists of 100 particles, each with a kinetic energy of 2 Joules. What’s the internal energy?

E = S KE

Answer: E = 2 x 100 = 200Joules.

Temperature = Average KE• Units depend of what scale you use• T = E/N where N = # particles and E = internal

energyExample: A gas sample consists of 100 particles, each with a kinetic energy of 2 Joules. What’s the internal energy? What’s the temperature?

Answer: E = 2 x 100 = 200Joules.

T = E / 100 = 2 degrees.

Heat = energy transferred due to a temperature difference• Heat flows only from a warmer object to a cooler one.• Units are Joules or calories.• Q is the symbol for heat.

A gas sample consists of 100 particles, each with a kinetic energy of 2 Joules. If 300J of heat are added, what’s the new temperature?

Answer: E = 200J + 300J = 500J.

T = E / 100 = 5 degrees.

Note: the temperature increases if heat is added, as expected.

Heat Transfer Processes Heat energy can be transferred from one body to another in three different ways.

• Conduction: Energy is transferred when two objects are in direct contact. Molecules of the hotter object bump into molecules of the colder object and cause them to speed up, warming the colder object.

• Convection: Energy is transferred from one body to a cooler one via currents in a fluid (a gas or liquid).

• Radiation: All objects, at any temperature, radiate electromagnetic radiation (light of visible and invisible wavelengths). Unlike conduction & convection, no medium (matter of any type) is necessary for heat transfer through radiation. Objects absorb radiation as well. At thermal equilibrium it will absorb as much as it radiates.

Sense of Touch• Sensations of cold or hotness are not

reliable temperature readings.• Sensations of cold or hotness tell you

about heat flow.If you put one hand in hot water, the other in cold, and then both in room temperature water, each hand tells you something different.

Which hand feels cool, and which feels warm?

ConnectionHow is convection important in cooking?

Starter

Compare an iceberg to a cup of hot coffee. a. Which has the greatest internal energy? b. Which has the greatest temperature?

Temperature ScalesFahrenheit: water freezes at 32 °F; boils at 212 °FCelsius: water freezes at 0 °C; boils at 100 °C

So, DF / DC = 180 / 100 = 9/5 = 1.8

This means, a one degree step in Celsius is a 1.8 degree step in Fahrenheit. OR, a one degree step in Fahrenheit, is a .56 step in Celsius.

F = 32 + (9/5)C C = 5/9 (F – 32)

There’s a problem with the Celsius and Fahrenheit Scales, and our definition of

temperature as Average KE.

What’s twice as hot as 40 degrees C?What’s twice as hot as zero degrees C?What’s twice as hot as -10 degrees C?

Absolute Zero & the Kelvin ScaleThe Kelvin scale is setup so that its zero point is the coldest possible temperature--absolute zero, at which point a substance would have zero internal energy. This is -273.15 °C, or -459.69 °F. Absolute zero can never be reached, but there is no limit to how close we can get to it. Scientists have cooled substances to within 10-5 Kelvin of absolute zero. How do we know how cold absolute zero is, if nothing has ever been at that temperature? The answer is by graphing Pressure vs. Temperature for a variety of gases and extrapolating.

P

T (°C)

gas A

gas B

gas C

-273.15 °C 0 °C

A gas exerts no pressure when at

absolute zero.

Starter

Compare an iceberg to a cup of hot coffee. a. Which has the greatest internal energy? b. Which has the greatest temperature?

Heat Units - Calories and Joules

Calorie - the amount of heat that will raise the temperature of 1 gram of water by 1 degree C.

1 calorie = 4.184 JSystems of Units Used:

Calories and grams, Joules and grams or Joules and kg.

Specific Heat cWhen heat is added to a substance its temperature

rises.How much will it rise?

Q = heat addedDT = temperature changeM = mass of the substanceC = the specific heat of the substance

Q = mcDT

Some Specific Heats

Example How much heat must be added to 500g of aluminum to take it

from 25 degrees Celsius to 125 degrees Celsius?

c = .215 cal / g oC DT = Tf – Ti = 125 – 25 = 100 oC

m = 500g

Q = mcDT = 500(.215)(100) = 10750cal

Example If 500cal of heat are added to 100g of lead at 25 degrees Celsius, what

will its final temperature be?

c = .031 cal / g oC DT = Tf – Ti = Tf – 25

m = 100g

Q = mcDT , 500 = 100(.031)(Tf – 25)

Tf = ((500)/(100)(.031)) + 25 = 161 + 25 = 186oC

Method of MixturesIf you mix two different substances together and they reach a common final temperature, then

Q1 + Q2 = 0

Or m1c1DT1 + m2c2DT2 =0

ExampleA 100g piece of metal at 150 degrees C is added to 500 grams of water at 20 degrees C. The metal and water end up at30 degrees C. What was the specific heat of the metal? mwcwDTw+ mmcmDTm =0 500(1)(30 -20) + 100c(30-150) = 0 5000 – 12000c = 0 c = .416 cal/gC

StarterWhen a pot of water is placed on the stove, it heats and begins to boil at 100 degrees Celsius. As the water continues to boil, the temperature

a. Slowly rises.b. Stays the same.c. Will drop slowly.

Latent Heat

Latent HeatThe word “latent” comes from a Latin word that means “to lie hidden.” When a substance changes phases (liquid solid or gas liquid) energy is transferred without a change in temperature. This “hidden energy” is called latent heat. Q = mcDT does not apply during a phase change.

Latent Heat Formula

Example: Lf (the latent heat of fusion) for water is 80 cal/g.

Ice melts at 0ºC. 50 grams of ice at 0ºC will not become liquid until additional heat is added. The amount of heat needed is:

Q = mLf = 50(80) = 4000 calIn other words, it takes 4000 calories of heat to turn 40 grams of ice at zero degrees C into 40 grams of water at zero degrees C.

Q = m Lf or Q = m Lv Q = thermal energy m = mass L = heat of fusion or vaporization

Latent Heat For Water

Lf = 80 cal / g = 3.35 x 10 5 J/kg

Lv = 540 cal / g = 22.6 x 10 5 J/kg

Find the heat required to turn 100g of ice at -20 degrees C to 100 g of steam at 120 degrees C.1st : Get the ice to its melting temp, 0 degrees C. Q = mcDT = 100 ( .5) ( 0 – (-20)) = 1000 cals2nd: Melt the ice Q = mLf = 100(80) = 8000 cals

3rd: Heat the water to 100 degrees Q = mcDT = 100 ( 1) ( 100 – 0 ) = 10000 cals4th: Turn the water into steam Q = mLv = 100(540) = 54000 cals

5th: Heat the steam Q = mcDT = 100 ( .48) ( 120 – 100) = 960 cals

GRAND TOTAL = 1000 + 8000+ 10000 + 54000 + 960 = 73960 cal