Chapters 19, 20

Temperature, Heat, and the First Law of Thermodynamics

Temperature

• Thermodynamics – branch of physics studying thermal energy of systems

• Temperature (T), a scalar – measure of the thermal (internal) energy of a system

• SI unit: K (Kelvin)

• Kelvin scale has a lower limit (absolute zero) and has no upper limit

William Thomson(Lord Kelvin)

(1824 - 1907)

Kelvin scale

• Kelvin scale is defined by the temperature of the triple point of pure water

• Triple point – set of pressure and temperature values at which solid, liquid, and gas phases can coexist

• International convention:T of the triple point of water is

KT 16.2733

The zeroth law of thermodynamics

• If two (or more) bodies in contact don’t change their internal energy with time, they are in thermal equilibrium

• 0th law of thermodynamics: if bodies are in thermal equilibrium, their temperatures are equal

Measuring temperature

• Temperature measurement principle: if bodies A and B are each in thermal equilibrium with a third body C, then A and B are in thermal equilibrium with each other (and their temperatures are equal)

• The standard temperature for the Kelvin scale is measured by the constant-volume gas thermometer

Constant-volume gas thermometer

ghPP 0

CPT

33 CPT

33 P

PTT

3

16.273P

PK

Celsius and Fahrenheit scales

• Celsius scale:

• Fahrenheit scale:

Anders Cornelius Celsius

(1701 - 1744)

Gabriel DanielFahrenheit

(1686 - 1736)

15.273TTC

325

9CF TT

Thermal expansion

• Thermal expansion: increase in size with an increase of a temperature

• Linear expansion:

• Volume expansion:

TL

L

3

TV

V

Thermal expansion

Chapter 19Problem 5

A copper telephone wire has essentially no sag between poles 35.0 m apart on a winter day when the temperature is – 20.0°C. How much longer is the wire on a summer day when T = 35.0°C?

Temperature and heat

• Heat (Q): energy transferred between a system and its environment because of a temperature difference that exists between them

• SI Unit: Joule

• Alternative unit: calorie (cal): Jcal 1868.4 1

Absorption of heat

• Specific heat (c): heat capacity per unit mass

• Common states (phases) of matter: solid, liquid, gas

• Latenet heat (L): the amount of energy per unit mass transferred during a phase change (boiling, condensation, melting, freezing, etc.)

)( if TTcmTcmQ

LmQ

Q Q

Absorption of heat

Q Q

Absorption of heat

Absorption of heat

Chapter 20Problem 17

A 1.00-kg block of copper at 20.0°C is dropped into a large vessel of liquid nitrogen at 77.3 K. How many kilograms of nitrogen boil away by the time the copper reaches 77.3 K? (The specific heat of copper is 0.0920 cal/g °C. Thelatent heat of vaporization of nitrogen is 48.0 cal/g.)

Avogadro’s number

• Mole – amount of substance containing a number of atoms (molecules) equal to the number of atoms in a 12 g sample of 12C

• This number is known as Avogadro’s number (NA):

NA = 6.02 x 1023 mol -1

• The number of moles in a sample

N – total number of atoms (molecules)m – total mass of a sample, m0 – mass of a single atom (molecule); M – molar mass

Amedeo Avogadro(1776 -1856)

M

m

Nm

m

N

Nn

AA

0

Ideal gases

• Ideal gas – a gas obeying the ideal gas law:

R – gas constant

R = 8.31 J/mol ∙ K

kB – Boltzmann constant

kB = 1.38 x 1023 J/K

nRTPV

nRTPV RTNN A )/( TNRN A )/( TNkB

TNkPV B

Ludwig EduardBoltzmann

(1844-1906)

Heat and work

Thermodynamic cycle

sdFdW

dsPA )( )(AdsP PdV

f

i

V

VPdVW

Heat and work

• Work is done by the system:

• Work is done on the system :

f

i

V

VPdVW

f

i

V

VPdVW

The first law of thermodynamics

• Work and heat are path-dependent quantities

• Quantity Q + W = ΔEint (change of internal energy)

is path-independent

• 1st law of thermodynamics: the internal energy of a system increases if heat is added to the system or work is done on the system

WQEEE if int,int,int

The first law of thermodynamics

• Adiabatic process: no heat transfer between the system and the environment

• Isochoric (constant volume) process

• Free expansion:

• Cyclical process:

WWE 0int

QQE 0int

000int E

0int WQE

WQ

Chapter 20Problem 29

Consider the cyclic process depicted in the figure. If Q is negative for the process BC and ΔEint is negative for the process CA, what are the signs of Q, W, and that are associated with each process?

Heat transfer mechanisms

• Thermal conduction

• Conduction rate:

• Thermal resistance:

• Conduction through a composite rod:

L

TTkA

t

Q chcond

P

2211 // kLkL

TTA chcond

P

k

LR Thermal conductivity

21 RR

TTA ch

Heat transfer mechanisms

• Thermal radiation

• Radiation rate:

• Stefan-Boltzmann constant:

• Absorption rate:

4eATrad P

4envabs eATP

428 /1067.5 KmW

)( 44 TTeA env Josef Stefan(1835-1893)

radabsnet PPP

Emissivity

Chapter 20Problem 46

At high noon, the Sun delivers 1000 W to each square meter of a blacktop road. If the hot asphalt loses energy only by radiation, what is its steady-state temperature?

Heat transfer mechanisms

• Convection

Heat transfer mechanisms

Questions?

Answers to the even-numbered problems

Chapter 19

Problem 2(a) 810°F(b) 450 K

Answers to the even-numbered problems

Chapter 19

Problem 61.20 cm

Answers to the even-numbered problems

Chapter 19

Problem 18(a) 2.99 mol(b) 1.80 × 1024 molecules

Answers to the even-numbered problems

Chapter 20

Problem 26(a) 12.0 kJ(b) –12.0 kJ