Heat and Heat Transfer

Something besides work

§ 17.5–17.7

Announcements

• Exam 3 this evening– CR 306– 5–7 PM

• It’s course evaluation time– Watch for e-mail notification

CPS Question

A. Transfer of force.

B. Transfer of momentum.

C. Transfer of mass.

D. Transfer of energy.

What is work?

Mechanical Equivalent of Heat

James Joule’s life-long obsession

Identical effects of adding heat to a system and doing work on it.

Source: Griffith, The Physics of Everyday Phenomena

CPS Question

A. Its speed increases.

B. Its height increases.

C. Its temperature increases.

D. Its energy does not change.

When heat is added to an object, how does the object’s energy change?

Heat

• Energy transferred because of a temperature difference

high T low Theat

• Zero heat flow at thermal equilibrium

CPS Question

What is the direction of heat flow?

A. From an object at high temperature to an object at low temperature.

B. From an object with high energy to an object with low energy.

C. Either one, because they mean the same thing.

Group CPS Question

A 10-kg copper block and a 1-kg copper block begin at the same temperature. and to each is added 100,000 J of heat is added to the 10-kg block, and 30,000 J of heat is added to the 1-kg block. The blocks are placed together in a perfectly insulating container. What happens?

A.Heat flows from the 10-kg block to the 1-kg block.

B.There is no net heat flow.

C.Heat flows from the 1-kg block to the 10-kg block.

D.It is impossible to determine.

Heat Units

• Joule

• Calorie (cal): heat needed to raise 1 gram of water 1 degree C (or K) = 4.184 J.

• British Thermal Unit (BTU): heat needed to raise 1 pound of water 1 degree F = 1054.35 J

Another Heat Unit

• U.S. Food Calorie: Cal = 1000 cal

• Food energy values are often presented in kJ in other countries

Specific Heat (Capacity)

• Heat needed to change the temperature of a unit amount of a substance.

– q = heat input– m = mass of sample– t = temperature change

• Units: J/(kg K) or cal/(kg K)

• Intensive

c =q

mT

Group Work

Healthy people can sit in a sauna with an air temperature of 200 °F for over 20 minutes without harm. Sitting in a hot tub with a water temperature of 200 °F would be quickly lethal. Why is there such a difference?

Example Problem 17.xx

An engineer working on a new engine design needs 1.6 kg of aluminum and 0.3 kg of iron for a moving part designed to operate at 210 °C. How much heat is required to raise its temperature from 20 °C to 210 °C?

Phase Changes

• Potential energies:

• During a phase change, potential energy, not kinetic energy (temperature) changes.

• Heating or cooling a changing phase does not change its temperature!

Solid

Liquid

Gas

ice

Liquid water

steam

Water temperature with heating

-100

-50

0

50

100

150

200

0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06

heat input (J/kg)

tem

pera

ture

(C

)

Heating Curve for Water

Water boils

Ice melts

335 kJ/kg

2,255 kJ/kg

Fermi Problem

•Suppose all of the earth’s oceans warmed by 0.1 °C. Is this amount of heat sufficient to melt the polar ice caps?

Heat Transfer Mechanisms

• Conduction: kinetic energy transferred by collisions between molecules

• Convection: energy transfer by mixing hot and cold materials

• Radiation: energy transfer by emission and absorption of electromagnetic waves

CPS Question

Solids conduct heat better than gases do. So why does a coat keep you warm in winter?Add together the numbers of the correct answers and enter the sum.

1. The coat reduces conduction.

2. The coat reduces convection.

4. The coat reduces radiation.

CPS Question

Hot applesauce takes longer to cool than the same quantity of hot water in the same pot. Why?Add together the numbers of the correct answers and enter the sum.

1. Conduction is slower in applesauce.

2. Convection is slower in applesauce.

4. Radiation is slower in applesauce.

CPS Question

Aluminized Mylar blankets actually can keep you pretty warm. Which heat transfer mechanism(s) do they reduce?Add together the numbers of the correct answers and enter the sum.

1. The blanket reduces conduction.

2. The blanket reduces convection.

4. The blanket reduces radiation.

CPS Question

A thermos bottle keeps hot things hot, and it keeps cold things cold. But how does it know?Add together the numbers of the correct answers and enter the sum.

1. It reduces heat transfer by conduction.

2. It reduces heat transfer by convection.

4. It reduces heat transfer by radiation.

Heat Current

H dQ/dT = –kA T/L

k = thermal conductivity

A = cross-sectional area

T = temperature difference

L = transport distance

negative sign: high T low T

T1 T2Q

L

• Newton’s law of cooling

Non-Uniform Body

H dQ/dT = –kA dT/dx

T1 T2Q

L

Example Problem 17.113

b) Show that the thickness of the ice sheet formed on the surface of a lake is proportional to the square root of the time to freeze if the heat of fusion of the water freezing on the underside of the ice sheet is conducted through the sheet.

c) If the upper surface of the ice sheet is at –10 °C and the bottom surface of ice resting on the water is at 0 °C, how long will it take to form an ice sheet 25 cm thick?

d) If the lake is 40 m deep, how long would it take to freeze the entire lake?

The air temperature is below 0 °C, and the water surface freezes.