Heat Transfer

Physics 202Professor Lee

CarknerLecture 14

PAL #13 First Law Final temperature of 20 g, 0 C ice cube dropped into 300 g of hot tea

at 90 C. Add up all heats (Q = cm T and Q = Lm) Heat 1: melt ice

Q1 = (333000)(0.02) = 6660 J Heat 2: warm up now melted ice cube

Q2 = (4190)(0.02)(Tf-0) Heat 3: cool down tea

Q3 = (4190)(0.3)(Tf-90) Step 4: add up heat

Q1 + Q2 + Q3 = 0

6660 + 83.8Tf + 1257Tf –113130 = 0

1340.6Tf = 106470

Tf = 79.4 C

Water condenses out of the air onto a cold piece of metal. Due to this condensation, the temperature of the air around the metal,

A) IncreasesB) DecreasesC) Stays the sameD) Fluctuates unpredictablyE) It depends on the temperature of the

metal

Ten joules of heat are added to a cylinder of gas causing the piston at the top to rise. How much work does the piston do?

A) 0 JoulesB) 5 JoulesC) 10 JoulesD) -10 joulesE) You cannot tell from the

information given

Which of the processes in the diagram produces the least work?

A) 1B) 2C) 3D) 4E) All are the same

Which of the processes in the diagram involves the least heat?

A) 1B) 2C) 3D) 4E) All are the same

Heat Transfer How is heat transferred from one place to

another? What is moving?

In heat transfer the analogous methods are convection and conduction

both a particle and a wave (but not really)

Conduction

The end in the fire experiences a large vibration of the molecules of the metal

This is called conduction The movement of heat from a high

temperature region to a low temperature region through another material

Conduction Through a Slab

Conductive Heat Transfer The rate at which heat is transferred by

conduction is given byH = Q/t = kA (TH - TC)/L

Where: Q is heat and t is time A is the cross sectional area of the material (in

the direction of heat transfer) T is the temperature (hot or cold)

Thermal Conductivities Metals generally have high k

For Al, k=235 for Cu, k=428 (W/ m K)

For air, k=0.026 for polyurethane foam, k=0.024 Down filled winter coats trap air for insulation

Composite Slabs

H = Q/t = A (TH - TC)/ (L/k) Where (L/k) is the sum of the

ratios of the thickness and thermal conductivity of each layer of the slab

Heat Loss Through a Wall

Radiation Energy can be directly transported by photons

The power (in Watts) that is emitted by an

object depends on its temperature (T), its area (A) and it emissivity ()

Pr = AT4

Where is the Stefan-Boltzmann constant = 5.6703 X 10-8 W/m2 K4

T must be in absolute units (Kelvin)

Absorption of Radiation

Pa =ATenv4

Any object thus has a net energy exchange rate with its environment of:

Pn = Pa -Pr = A(Tenv4 - T4)

Blackbody Radiation

They absorb all of the radiation incident on them

Every object whose temperature is above 0 K emits thermal radiation People emit thermal radiation at infrared

wavelengths and thus can be detected at night with IR goggles

Today’s PALa) Consider a house window

with a size of 1 meter by 1.5 meters and 0.75 cm thick. Inside the house it is 20 C and outside it is 10 C. Compare the heat loss through the window by both conduction and radiation. Which is greater?

b) Imagine you replace the window with a double-pane window composed of two 0.25 cm thick windows with 0.25 cm of air in between. What is the heat loss rate due to conduction now?

Convection Hot air (or any fluid) expands and

becomes less dense than the cooler air around it

If the hot air cools as it rises it will eventually fall back down to be re-heated and rise again

Examples: baseboard heating, boiling water, Earth’s atmosphere

Convection Rate Factors

Fluidity

Energy exchange with environment

How rapidly will the material lose heat?

A small temperature difference may result

in not enough density difference to move

Structure of the Sun

Core

Radiative Zone

Convective

Zone

Photosphere

Chromosphere

Corona

Heat Transfer in The Sun

Near the core (where the energy is produced via hydrogen fusion) energy is transported by radiation

About 75% of the way out, the opacity increases to a level where convection becomes dominant

Convection transports the energy to the surface where it radiates away into space

Next Time

Read: 19.1-19.7 Homework: Ch 18, P: 54, 57, Ch

19, P: 5, 7, 19