THERMAL PHYSICS

• Temperature and the zeroth Law of Thermodynamics• 2 objects are in thermal contact if energy can be exchange

between them• 2 objects are in thermal equilibrium if they are in thermal

contact and there is no net exchange of energy (ex: in fig)• Zeroth law of thermodynamics (law of equilibrium)

If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other.

Two objects in thermal equilibrium with each other are the same temperature

Thermometers and temperature scale

Review: - thermometers

-Celsius temperature scale( freezing point, boiling point)

The ct. Volume gas thermometer and the Kelvin scale

In a gas thermometer, the temperature reading are independent of the substance used in the thermometer

The behavior observed in this device is variation of pressure with temperature of a fixed volume of gas

• If the temperatures are measured with various gas thermometers containing different gases, the readings are nearly independent of the type of gas used

• The pressure extrapolates to zero when temperature is -273.16oC

P=0, T= -273.16oC –absolute zero

• Absolute zero is used for the Kelvin temperature scale Tc =T-273.15

• The triple point of water, which is the single temperature and pressure at which water, water vapor and ice can coexist in equilibrium

• SI unit T = K• Kelvin- define as 1/273.16 of

the temperature of the triple point of water

• The Celsius, Kelvin and Fahrenheit Temperature Scale

• 0oC=32oF; 100oC= 212oF

• TF=9/5 TC+32

• TC=5/9(TF-32)

• ΔTF=9/5ΔTC

• Thermal Expansion of solids and liquids• Thermal expansion: as temperature of the

substance increase its volume increase• If the thermal expansion of an object is

sufficiently small compared with the object ‘s initial dimensions, then the change in any dimenΔsion is proportional with the first power of the temperature change:

• ΔL =α L0ΔT; L0- initial length

• α- the coefficient of linear expansion for a given material

• SI unit (oC)-1

• Area: A0 =L02

• L=L0 +α L0ΔT

• A= L2 =(L0 +α L0ΔT)(L0 +α L0ΔT)= =L0 2+2α L0

2ΔT+ (α L0ΔT)2

• αΔT<< 1 , squaring it makes much smaller

• A = L0 2+2α L02ΔT

• A=A0+2α A0ΔT

• ΔA =γ A0 ΔT; γ =2α- coefficient of area expansion

• ΔV =β V0 ΔT; β =3α – coefficient of volume expansion

• Macroscopic description of an ideal gas• Ideal gas – is a collection of atoms or

molecules that move randomly and exert no long range forces on each other

• Each particle of the ideal gas is individually point-like, occupying a negligible volume (gas maintained at a low pressure or a low density)

• n-nr of moles- the amount of gas in a given volume

• NA=6.02x1023particle/mole- Avogadro’s number

• The number of moles: n= m /molar mass, m-mass, molar mass- the mass of one mole of that substance

• One mole of any substance is that amount of the substance that contains as many particles as there are atoms in 12g of the isotope carbon-12

• m atom = molar mass/NA

• Supposed an ideal gas is confined to a cylinder container

• I Boyle’s law: when the gas is kept at a constant T, its P is inversely proportional to its V (T=ct., P~V)

• II Charle’s Law: P = ct., V~T• III Gay Lussac's Law: V =ct, P~T• Ideal gas Law: PV=nRT

R-universal gas constant

R = 8.31 J/mol K (in P=Pa and V=cm3)

R=0.0821 L atm /mol K(1L = 103 cm3)

• n = N / NA , n- nr. of molecules, N-nr. of the molecules in the gas

• PV = (N / NA)RT

• PV = N kB T

• kB- Boltzmann's constant

• kB= R / NA= 1.38 x 10-23 J/K

• The kinetic theory of gases• 1. The number of molecules in the gas is large,

and the average separtion between them is large compared with their dimensions

• 2. The molecules obey Newton’s lows of motion, but as a whole they move randomly

• 3. The molecules interact only through short-range forces during elasstic collisions

• 4. The molecules make elastic collision with the walls

• 5. All molecules in the gas are identical

• Molecular model for the pressure of an ideal Gas

Δpx= m vx-(- mvx) =2 mvx

F1= Δpx/Δt = 2m vx/ Δt

Δt = 2d/vx

F1= 2m vx/ 2d/vx = m vx2/d

For N molecules:

vx2= (v1x

2+ v2x2+…+ vNx

2)/N

F= (Nm/d) vx2

vx2= 1/3 v2

F= N/3(mv2/d)

P = F/A =F/d2= 2/3(N/V)(1/2 mv2) =P

• P=2/3(N/V)(1/2 mv2) – the pressure is proportional to the number of molecules per unit volume and to the average transitional kinetic energy of a molecule

• Molecular interpretation of Temperature

PV= 2/3 N(1/2 mv2)

PV = N kB T

T= 2/(3kB) (1/2 mv2)- the temperature of gas is a direct measure of the average molecular kinetic energy of gas

1/2 mv2 =3/2 kB TKE total= N(1/2 mv2) =3/2 NkB TkB= R / NA; n = N / NA KE total= 3/2 n RT –the total transitional KE of the

system of molecules is proportional to the absolute temperature of the system

The Internal energy U for a monatomic gas: U= 3/2 n RT

The root-mean-square (rms) speed of the molecule

vrms=√ v2 = √3kBT/m= √3RT/M (M- molar mass)

• Ex: if a gas in a vessel consists of a mixture of hydrogen and oxygen, the hydrogen molecules with a molar mass of 2.0x10-2 kg/mol, move four time faster than oxygen molecules, with molar mass 32x10-3 kg/mol. IF we calculate the rms speed for Hydrogen at room temperature(300K):

vrms=√3RT/M =√3(8.31 j/mol K)(300K) /(2.0x10-2 kg/mol)= 1.9 x 103 m/s

This is 17% of escape speed for Earth