Whiteboard Work

1. The 2004 Tour de France’s Alpe d’Huez time trial was a climb with its finish 1200 m higher than the start. The winner, Lance Armstrong, and his gear had a combined mass of 84 kg.

 

The work Lance had to do was mgh =

(84 kg)(9.8 N/kg)(1200 m) = about 106 J.

a. Muscle is about 20% efficient, so Lance had to deplete 5 times as much potential energy as the work he produced. How much energy did he consume?

b. How much of the energy he consumed was not converted to work?

Heat and Phase Changes

Our interaction with the world of the small

What’s the Point?

• What happens to all our energy?

• How does energy convert in freezing, melting, evaporation, and condensation?

Objectives

• Define and differentiate heat and temperature.

• Explain the role of heat in conservation of energy.

• Describe the energy transfer of phase changes.

Mechanical Equivalent of Heat

James Joule’s life-long obsession

Identical effects of adding heat and doing work

Source: Griffith, The Physics of Everyday Phenomena

Heat and work

• Doing work on an object changes its energy.

• Heat transfer is another way to change an object’s energy!

• Work heat: easy

• Heat work: more difficult

Temperature and Energy

• Average translational molecular kinetic energy is

1/2 kBT

per mode of motion.

• kB = 1.3806610–23 J/K (Boltzmann constant)

• Individual molecules can have higher or lower kinetic energies than average.

Terms

• Temperature is proportional to average molecular translational kinetic energy.

• Internal energy (U) is total molecular kinetic + potential energy.

• Heat is molecular energy transferred from high to low temperature.

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

When a red-hot piece of iron is dropped into a bucket of water,

Poll Question

A. the water becomes hotter.

B. the water’s temperature increases .

C. the water’s internal energy increases .

D. the water receives heat from the iron.

E. all of the above.

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 J/(mol K)

• Intensive

c =q

mT

Using c

The temperature change T of an object to which an amount of heat q is added is

T = q/(mc)

where m is the object’s mass and c is its specific heat.

Whiteboard Work

2. The specific heat of Lance Armstrong is about the same as the specific heat of water: 4184 J/(kg °C).

If all the non-work energy he converted in the Alpe d’Huez climb stayed in his 75-kg body, by how many degrees would his body temperature have risen?

Another Heat Unit

• U.S. Food Calorie: Cal = 1000 cal

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

Quick Whiteboard Work

3. How many Calories (food calories) did Lance burn in the Alpe d’Huez climb?

Phase Changes

Phase Changes

• Melting, boiling, freezing, condensing…

• Added or removed heat changes the substance’s potential rather than kinetic energy

• Water freezes at 0 °C, boils at 100 °C (well, about 92 °C in Laramie)

• Not all heat transfer is expressed as a temperature change.

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)

temperature (C)

Heating Curve for Water

Water boils

Ice melts

Think Question

When are the molecules’ intermolecular potential energies highest?

A. When they are together in the liquid.

B. When they are separated in the gas.

Phase Changes

• Potential energies:

Solid < Liquid < Gas

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

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

Latent heat

• Potential energy of phase change (energy required to change the phase of 1 kg of substance)

• Water’s latent heat of fusion (melting):

335,000 J/kg

• Water’s latent heat of vaporization:

2,255,000 J/kg

Whiteboard Work

4. During the Alpe d’Huez climb, how much sweat would Lance have needed to evaporate to keep his body temperature constant?

The heat q needed to vaporize a mass m of water is

q = m (2.255  106 J/kg).Solve for mass m and substitute in the values.

Evaporation of a Liquid

• More energetic jostling = higher temperature

• An especially fast molecule at the surface may detach!

Evaporation of a Liquid

• More energetic jostling = higher temperature

• An especially fast molecule at the surface may detach!

Evaporation

• Evaporating molecules carry away energy

• KE PE

• Remaining liquid cools (KE decreases)

Reading for Next Time

• Thermodynamics

• Big ideas:– Why most processes are irreversible– Entropy