18 Heat and the First Law of Thermodynamics

• Heat Capacity and Specific Heat

• Change of Phase and Latent Heat

• Joule’s Experiment and the First Law of Thermodynamics

• The Internal Energy of an Ideal Gas

• Work and the PV Diagram for a Gas

• Hk: 31, 37, 47, 51.

Heat & Internal Energy

• heat is energy that flows due to temperature differences. SI Unit: joule

• internal energy is the total energy of an object in its center of mass reference frame

Specific Heat Capacity

• The amount of heat needed to raise 1kg by 1°C

• c = Q/mT SI Unit: J/kg·°C

• m = mass receiving (or emitting) heat

• T = temperature change

• Q = mcT

• /

Example: 300J of heat are added to 100grams of a substance. The temperature rises by 2.20 degrees C.

CkgJCkg

J

Tm

Qc

/1364

)20.2)(1.0(

300

The specific heat of the substance is:

Example: Calorimetry

Other Heat & Energy Units:

JcallbftBtu 10542527781

Jcal 184.41

CalJkcal 141841

calJatmL 22.243.1011

Example Conversion

WBtu

J

s

h

h

Btu3500

1054

3500

000,12

A Gas Range is quoted (incorrectly) as “12,000 Btu”. The equivalent power for an Electric Range in watts is:

Solid/Liquid Transformation

• Melting• Heat in• KE breaks bonds• Molecules move• Liquid forms

• Freezing• Heat out• Molecules lose KE• Settle in one place• Solid forms

8

Energy in Phase Change

• Energy added:

• solid liquid gas

• energy released:

• gas liquid solid

Liquid/Gas Transformations

• Evaporation• Highest KE molecules

escape liquid from surface

• Evaporative cooling, e.g. sweat evaporates cooling your body

• Boiling• Highest KE molecules

form gas bubbles throughout

• Hot gas bubbles rise and escape at surface

• Liquid has passed heat out, e.g. simmering at constant temperature

Latent Heat• Energy needed to melt or vaporize 1kg

of a substance.• Latent Heat, L = Q/m. • Q = mL.• Example: 2.5kg of ice at 0.0°C melts

into 2.5kg of water at 0.0°C.

)/5.333)(5.2( kgkJkgmLQ f

kJ830

Joule’s Experiment confirmed the mechanical equivalent of heat.

1st Law Thermodynamics

intbut feature new a isheat

: tocompare

EE

EW

sys

sysext

18-4 Internal Energy of Ideal Gas

• E-internal is proportional to the absolute temperature

• internal energy is in the kinetic energy of the molecules of the gas

• /

Work and the PV Diagram

Vf

Viongas PdVW

it.on done be work topositivefor order

in dV) (negative compressed bemust Gas

Gas Processes

• Isobaric = constant pressure

• Isometric (Isochoric) = constant volume

• Isothermal = constant temperature

• Ex.

Summary:

• specific heat is material dependent.

• latent heats; objects change phase at constant temperature.

• calorimetry: science of heat measurements

• 1st law of thermo. is energy conservation

• mechanical equivalent of heat

• Pressure x volume = work

Example: Human vs. Gasoline Engine

Lance Armstrong: 460W V8: 200hp

Power Ratio = 200hp/(460/746)hp = 332 times more

Lance: (460W)(21,600) = 9.9 MJ = 2370 Cal

Energy Consumption (6h = 21,600s):

V8: (332 times more) = 3.3 GJ = 788,000 Cal

Which of the following is a unit of heat?

1 2 3 4

0% 0%0%0%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1. N/m

2. N/m2

3. N·s

4. N·m

Heat is added to a system and the change in internal energy of the system is 1/3 of the heat added. Which of the following is true?

1 2 3

0% 0%0%

1. Work on system is +

2. Work on system is –

3. Work on system is 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

When not colliding, molecules of an ideal gas

1 2 3

0% 0%0%

1. Attract

2. Repel

3. Neither attract or repel

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

Molecules in an ideal gas

1 2

0%0%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1. Never collide

2. Sometimes collide

18-5Work and PV Diagrams

Work and PV

• [PV] = (N/m2)(m3)= joule = energy

• Work done by an expanding gas:

• Work done by gas during isothermal expansion:

f

i

V

Vby PdVW

i

fisothermalby V

VnRTW ln,

Internal Energy of an Ideal Gas

• is proportional to temperature of gas

• internal energy is in the kinetic energy of molecules of the gas