# Major Concepts in Physics Lecture 1

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```					Major Concepts in Physics
Lecture 14.
Prof Simon Catterall
Office 309 Physics, x 5978
smc@physics.syr.edu
http://physics/courses/PHY102.08Spring

PHY102                    1
Plan for today … quick tour of some
concepts of thermodynamics …
   Temperature, heat. Thermal equilibrium
   Ideal gases – gas laws
   Real gases – molecular interactions
   Internal energy, work and 1st law of
thermodynamics

PHY102
Temperature
   This is a measure of the mean kinetic energy
of the atoms/molecules that comprise body
   Simplest ex. Ideal gas. Gas comprises a
(very) large number of atoms in random
motion
N A  6.022  10 23 mol -1
   I mole=number atoms in 12 g of carbon
Assume all atoms move independently
except for collisions

PHY102
Absolute (Kelvin) temperature

   Mean kinetic energy=1/2m<v2> = 3/2 kT
k = 1.3810-23 J/K is
Boltzmann’s constant

<v2> means average squared speed
Same temperature scale we used for thermal
Square root of this is called the rms speed

PHY102
The distribution of speeds in a gas is given by the Maxwell-
Boltzmann Distribution.

PHY102
Example (text problem 13.70): What are the rms speeds of
helium atoms, and nitrogen, hydrogen, and oxygen
molecules at 25 C?

3kT
vrm s          On the Kelvin scale T = 25 C = 298 K.
m

Element     Mass (kg)        rms speed (m/s)
He     6.6410-27            1360
H2     3.32 10-27           1930
N2     4.64 10-26           515
O2     5.32 10-26           482

PHY102
Thermal equilibrium
A A                           BB
A
A                                              B
A
A

A AAAAMolecules mix and eventually attain same
Molecules mix and eventually attain same
A A             A
Mean kinetic energy – same temperature
AA A    A      Mean kinetic energy – same temperature!
A
f      f
h

PHY102
Gas demo - Heat

   Independent of size of ‘’atoms’’ and their
initial motion they all end up carrying same
energy after many collisions
   We often say that when two objects are
placed in thermal contact heat flows
between them until their temperatures are
equal
Heat is thus energy in transit

PHY102
Fig. 14.9a

PHY102
Pressure of ideal gas

   The pressure of a gas is a measure of the
mean force per unit area exerted by the
atoms of the gas on the walls of its container
   Arises as atom changes direction after
colliding with wall  change of momentum
   Depends on how many atoms are in
container and speed with which they move

PHY102
.

PHY102
Ideal gas law

   Find P=2/3 N/V x (mean kinetic energy K)
   Using K=3/2 kT 
P=(Nk)/V T=n(NAk)/V T
or
PV=nRT
where gas constant R=NAk=8.31 J/mole
n number of moles present

PHY102
Gas demos

   Pressure varies linearly with temperature

PHY102
Fig. 13.10c

PHY102
Internal energy U

   The internal energy of a gas/body is the sum
of all molecular energies
   For an ideal gas: just kinetic energy
   For real gas:
   Potential energy associated with intermolecular
forces (electrical in origin)
   Energy of vibration and rotation for molecules

PHY102
An ideal gas is compressed so that its
volume halves while keeping its
temperature constant. Does its internal
energy …
   Increase
   Decrease
   Stay the same

PHY102
Heating

 When heat Q is applied to body we will
increase its internal energy U
 Usually some of this internal energy is kinetic
and hence its temperature T increases
T1T2
 Typically:

Q=mC(T2-T1)
m= mass, C = specific heat capacity. Depends
on substance ..

PHY102
Example (text problem 14.12): If 125.6 kJ of heat are
supplied to 5.00102 g of water at 22 C, what is the final
temperature of the water?

Q  mcT  mcTf  Ti 
Q
Tf  Ti 
mc
125.6 kJ
 22C                            82C
0.5 kg4.186 kJ/kg C

PHY102
Work
   There are two ways to increase internal
energy of body – either by adding heat Q OR
   Doing work on the body eg compressing it
   Imagine molecules connected by little
springs. Compress the system a little – this
takes mechanical work (PHY101). It
increases the stored energies in these
molecular springs. After the springs relax will
also increase molecular kinetic energy.

PHY102
Work on a gas

   Work done compressing a gas at constant
pressure from V1 to V2 is just P(V1-V2)
   Think of gas in cylinder contained by piston
V=Ax. W=Fx=(F/A) Ax=P(V1-V2)

x

V2

V1
PHY102
1st   law of thermodynamics

   Generalizes conservation of
(mechanical+electrical) energy learnt in
PHY101 to all types of energy
   Specifically including heat Q and internal
energy U.
   Write
U=Q+W

PHY102
Fig. 14.3

PHY102
Demo
   Electrical power=current x voltsconverted
to heat
   Heat transferred to water  raises its internal
energy U
   Leads to change in temperature
   Calculate amount of electrical heat applied.
   Calculate heating of liquid from specific heat
capacity  Find they are equal
Conservation of energy!!

PHY102
Summary

   Temperature as kinetic energy of molecular
constituents.
   Ideal gas model: atoms in rapid, random motion 
molecular description of pressure, Ideal gas
equation
   Internal energy: kinetic plus internal potential energy
(real gases ….)
   Change U thru heat Q and/or work W
    1st law of thermodynamics – energy is conserved!

PHY102

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