Chapter 14: Heat

Chapter Outline

• Heat as energy transfer• Temperature vs. heat vs. internal energy• Internal energy of an Ideal Gas• Specific Heat• Calorimetry• Latent Heat• Heat Transfer: conduction, convection, and

radiation

Heat is a Transfer of energy

• Heat always flows from hot to cold.• In the 18th century scientists believed heat was

an actual, physical thing that flowed from one object to another.– They pictured it as a fluid and named that fluid

caloric• The scientists were never able to detect this

fluid.

The New Model

• Scientists never discovered caloric because heat is not a physical object.

• In the 1800s several scientists worked on a new model of heat, one such scientist was an English brewer named James Prescott.

• Prescott filled a vessel with water that had paddles in it that would move when a mass was dropped.

The Result

• What Prescott discovered was that the temperature of the water increased.

• Prescott showed that mechanical energy is transferred from one object to another as heat.

• What we have been calling the moss-pit is the transfer of heat.

Units of Heat

• calorie: the energy needed to heat 1g of water 1C

• Calorie (aka Kilocalorie aka food calorie): the energy needed to heat 1kg of water 1C

• 1 calorie = 4.186J• 1 kilocalorie(kcal) = 4186J• These bottom 2 conversions show how heat IS

energy

Please Consider the Following

• If heat is energy and work is the exchange of energy, then can heat do work?

Example 1

• How tall a flight of stairs would a person have to climb to burn off 500 Calories? Assume the person is 60kg.

Solution

• Step 1 – convert Cal to J• 500kcal (4186J/kcal) = 2.1E6J

• So 500 Calories gives us 2.1E6J of work, how high will that work take us?

• Step 2 W = mgh• h = W/mg = 2.1E6J / (60kg x 9.8m/s2) =

3600m or over 11,000 ft!

Conversation of Energy

• Heat factors into the conversation of energy• If any kinetic energy is lost, it is lost as heat.• KEi = KEf + Q, where Q is heat, (why Q? I don’t

know)

Example

• A 3.0g bullet travelling with a speed of 400m/s passes through a tree and slows down to 200m/s. How much heat, Q, is produced and shared by the bullet to the tree?

Solution

• Step 1: convert to kg• 3.0g = 3.0E-3kg

• Step 2: KEi = KEf + Q• Q = KEi - KEf

• Q = 1/2mvi2 – 1/2mvf

2

• Q = 1/2m(vi2 – vf

2) • Q = 180J = 43cal

Temperature, Heat, and Internal Energy

• The sum total of all the energy of all the molecules in an object is called the internal energy.

• Remember, temperature is the average kinetic energy of all molecules in an object.

Consider This

• If you touch a glass of water that is the same temperature as your hand is there heat transfer?

• Does the water have internal energy?

Internal Energy of an Ideal Gas

• The internal energy of an ideal gas, U, depends only on the temperature of the gas and how many moles of gas there are.

• U = 3/2nRT• Again this is for an ideal, monatomic gas.• For a real gas, rotational and vibrational

energies would come into play.

Heat and Temperature

• As heat is put into an object the temperature goes up.

• But by how much? • Well that depends…

Some questions to ask

• Is there a difference to how long it takes to boil a pot of water if it is a little pot or a big pot?

• Does it take more or less energy to get heavier molecules moving?

• Will it take more heat to get to a higher temperature?

The math

• Q = mcΔT, where m is mass, T is temperature, and c is called specific heat and is different for every element.

• c = Q/mΔT and its units are J/kgCo

Heat and conservation of energy

• Imagine a completely isolated system where no energy can flow into or out of the system.

• In such a system the energy must be conserved.

• So, if heat is lost by one part of the system it must be gained by another part.

Calorimetry

• Heat lost = heat gained• Remember from yesterday, Q = mcΔT• So mc(Tf – Ti) = mc(Tf – Ti)

Example

• If 200cm3 of tea at 950C is poured into a 150g glass cup initially at 250C, what will be the final temperature T of the mixture when equilibrium is reached, assuming no heat flows to the surroundings?

Solution part 1

• We need to find m, c, and ΔT• m: mass is density times volume so

m = 200E-6m3 x 1E3kg/m3 = 0.20kg• c = 4186J/kgC (because tea is basically water)• Conservation of energy gives us

mteactea(950C – T) = mcupccup(T – 250C)

Solution part 2

• mteactea(950C – T) = mcupccup(T – 250C)• (0.20kg)(4186J/kgC)(95 – T) =

(0.15kg)(840J/kgC)(T – 25)• Solving for T gives us T = 890C

Finding Specific Heats

• What could you do to find the specific heat of an unknown substance?

What scientists do

• They perform what is called calorimetry– They heat the object to a certain temperature.– They quickly place the hot object into an amount

of water whose mass and temperature are known.– They record the final temperature of the water to

see how much energy was transferred.• Important, when doing this, scientists try to

keep the system well insulated from the outside environment.

The details

• Heat lost by sample = heat gained by water + heat gained by the container

• msamplecsampleΔTsample = mwatercwaterΔTwater + mcupccupΔTcup

Example

• We want to know the specific heat of a new metal alloy that we created. A 0.150kg sample of the new alloy is heated to 5400C. It is then placed in 400g of water at 100C, which is contained in a 200g aluminum calorimeter cup. If the final temperature of the water is 30.50C, what is the specific heat of our alloy?

Solution

• msamplecsampleΔTsample = mwatercwaterΔTwater + mcupccupΔTcup

• (0.150kg)(csample)(540 – 30.5) = (0.400kg)(4186J/kgC)(30.5 – 10) + (0.200kg)(900J/kgC)(30.5 – 10.0)

• 76.4csample = (34,300 + 3700)J/kgC

• csample = 500J/kgC

Bomb calorimeter

• A bomb calorimeter is used to measure the heat released when a substance burns or explodes.

• It is used to find the calorie content of foods or the energy released by a type of explosive.

• A carefully weighted sample of the substance, together with an excess of oxygen at high pressure, is placed in a sealed container (the bomb) which is placed in the water and ignited.

Conduction

• Heat transfer by molecules colliding• The flow of heat is related to the difference in

temperature

• Where l is the distance between the ends of the two objects, A is the area, and k is called the thermal conductivity, which is different for different materials

l

TTkA

t

Q 21

Conductors vs. Insulators

• Materials that have a high k transfer heat quickly and are called conductors.

• Materials that have a low k transfer heat slowly and are called insulators.

Vive la Resistance

• Insulators commonly have an R value assigned to them to illustrate how good an insulator they are.

• The higher the R, the better the insulator• R = l/k where l is the thickness of the material

and k is its thermal conductivity

Convection

• Heat transfer by the mass movement of molecules from one place to another.

• 2 types– Forced: like a furnace blowing hot air into a room– Natural: warm air rises

Radiation

• Heat transfer that requires no medium at all.• This is how the sun transfers its heat to earth

or how IR lamps keep food warm

Stefan-Boltzmann equation

4ATet

Q

Where σ is called the Stefan-Boltzmann constant, σ = 5.67E-8W/m2K4 and e is called the emissivity and is between 0 and 1

More on emissivity

• Dark objects like black clothing or dark roofs have an emissivity close to 1 and absorb radiation

• Light objects like white roofs reflect radiation

Going Tanning

• The sun sends 1350J of energy per second per square meter at a right angle to the earth.

• About 1000W/m2 reaches the surface. • The following equation can be used to find

how much radiation an object absorbs from the sun.

cos)/1000( 2 eAmWt

Q