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

JTmQc

/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

WBtuJ

sh

hBtu 35001054

3500000,12

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/m2. N/m2

3. N·s4. 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. Attract2. Repel3. 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 collide2. 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