## Classical Mechanics: Lecture 32 Notes

**Overview**

Today is a 49 minute lecture on thermometric properties.

**Details **

Most substances expand upon heating and shrink upon cooling.

A rod of length L is placed in ice and then in boiling water. L1 is shorter. L2 is longer. This is the Celsius measuring system. You can make a plot of temperature by length.

0 C = 32 F

100 C = 212 F

T f = 9Tc/5 + 32

Room temperature is 20 C or 68 F.

-40C = – 40F

Absolute zero is -273.15 C or -460 F.

**C F K**

20 68 293

-273 -460 0

Most substances expand when heated.

dL = a L dt

a is the linear expansion coefficient. Varies as the substance changes:

Brass 19

Cu 17

Pyrex 3.3

Invar 0.9

Steel 12

all times 10^-6/C

Invar is a mixture of 65% iron, 35% nickel.

Railroad expansion, a rail of 1000 meters. dT = 50 C

dL = .06 meters or 60 cm

It wants to bulge up or down. There are openings between rails of 5 cm. 12 openings to cover the distance. They make a sound when run over. Bridges have expansion joints.

A bimetal is a strip of two metals attached together.

dL cu – dL invar = (a cu – a inv) L dT

if T = 100C, L = 10cm. The invar will curve. These are used in thermostats and in safety valves.

A coil with a tube at the end, containing mercury. There are two wires which go to the heating system, the heater is on. The bimetal tightens, the mercury rolls out. 30 minutes in. The contacts are open, the heating stops.

From linear to cubic expansion. What is the volume increase? A cube, all sides L. The whole volume is L3. New volume is (L + dL)3 or L3(1 + dL/L)

(1+x)^n = 1 +nx when n<<1

Fill a narrow glass tube with mercury. Radius 1 mm, volume of mercury of 1 cm^3.

pi r^2 dh is the volume of the new column.

Shrink fitting is heating a ring, make it expand, then fit it around a cylinder, let it cool.

Water is different. Ice is 8% less dense than water, so it floats. The density of ice is 0.92 grams/cm^3. The density of water is 1 gram/cm^3.

**Review**

p = mv

F = ma

P = IV

V = IR

t=1/f

w = 2 pi f

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