Temperature and Heat -------------------------------     Joseph F. Alward, PhD       Department of  Physics     University of the Pacific

Lord Kelvin

   Fahrenheit and Celsius

F = (9 / 5) C + 32             -----------------------------------------------------------------   Example 1:  What is 100 C in Fahrenheit ?     (9 / 5)100 + 32 = 180 + 32 = 212 F -----------------------------------------------------------------  Example 2:  At what temperature do the  Fahrenheit and Celsius scales read the same?                    x = (9 / 5) x + 32   (- 4 / 5) x  = 32                x  =  - 40          - 40 C is the same temperature as - 40 F

  Celsius and Kelvin

K = C + 273

Example 1: What is 100 C in Kelvin?                        100 + 273.15 = 373.15 K -------------------------------------------------------- Example 2:  What is 0 K in Centigrade?   C = K - 273.15       = 0 - 273.15       = -273.15 William Thomson (Lord Kelvin)  1824-1907

   Absolute Zero

No motion or pressure at -273.15 C Absolute zero :  O K

 Example Problem        

What is the pressure when the  temperature is -100 C? (1 Pascal = 1 N/m2)

The equation of a straight line:        y = mx + b         P = mT + P0 4000 = m(0) + P0  (drop units)     P0 = 4000 Pa ----------------------------------------- 0 = m(-273.15) + 4000 m = 4000/273.15     = 1.46 Pa/C ----------------------------------------- P = 1.46 T + 4000 P = 1.46(-100) + 4000    = 3854 Pa

  Thermal Expansion

Bridge expansion joint.   In August the teeth will mesh together.

Concrete patio buckles. No    expansion gap was included.

This track was laid in   February; the picture was taken in August.

   Linear Expansion

Space between slabs of concrete in sidewalk   allows expansion in the summer.

Railroad track expansion joint

 Oil Pipe Line

   Hole Expansion

  Hole Expansion Explained

  Coefficient of Linear Expansion

DL = aLDT        a = coefficient of linear expansion [C-1]

Example:  Steel rod                     L = 5 meters  a = 11 x 10-6 C-1  T0  = 25 C      T = 55 C --------------------------------  DT = 55 C - 25 C        = 30 C DL = aLDT       = 11 x 10-6 C-1               x 5 m (30 C)       = 1.65 x 10-3 m       = 1.65 mm

 Linear Expansion Example          

T0 = 28 C At what temperature will the gap be closed? ------------------------------------------------------------ Brass:        19 x 10-6 C-1 Aluminum:  23 x 10-6 C-1

DL = aLDT DLBrass + DLAluminum = 0.002 m 19 x 10-6 (1.5)DT +            23 x 10-6 (0.8)DT = 0.002  DT = 42.64 C     T = 28 + 42.64        = 70.64 C

  Volume Expansion

   Volume Expansion

Atoms have small amplitude   of vibration at low temperature.

At higher temperature, atoms have   larger amplitude of vibration.

  Volume Expansion

Problem:   What is the change in volume of an aluminum sphere of radius r = 20 mm whose temperature changes from 50 C to -40 C?

b = 72 x10-6 C-1 DV =  bV0DT  V0 = (4/3)pr3       = 33,500 mm3 DT = - 90 C (negative) DV = -217 mm3

  Coefficients of Area and Volume Expansion

Rectangle L0   = initial length W0  = initial width DT  = change in  temp DL  = change in length DW = change in width    L = L0 + DL       =  L0 + aL0DT   W = W0 + DW        =  W0 + aW0DT

DA  = A - A0        =  (L0 + aL0DT)( W0 + aW0DT) - L0W0        =  L0W0 + 2a L0W0DT + a2 L0W0(DT)2 - L0W0        =  (1 + aDT/2)2a L0W0DT Note:  a = 10-6 C-1 typically         DT < 50 C typically     Ignore a DT/2 compared to 1: DA  = 2a L0W0DT         = 2a A0DT         =    gA0DT     g  = coefficient of area expansion      = 2a     b  = coefficient of volume expansion = 3a What are the units of these coefficients?

   Loosening a Tight Nut

A nut is very tight on a screw. How shall it be loosened?  By heating, or by cooling?

The nut expands, the screw expands, and the space expands.  Shrink-fit iron rims on wooden wheels.

   Expansion of Glass

Boiling Water Breaks Ordinary Glass Cup Pyrex has one-third the coefficient of expansion of ordinary glass.

Expansion Coefficients  of Selected Materials   Material   Linear Expansion Coefficient  a      x 10-6 C-1 Aluminum         24 Brass         19 Concrete         12 Steel         11 Glass (ordinary)           9 Glass (Pyrex)        3.2

  Bimetallic Strips

A bi-metallic strip two layers of two different metals. Brass:     a = 19  x 10-6 C-1     Steel:      a = 11 x 10-6 C-1

Brass side expands more than steel when heated, and contracts more when cooled.

 Bimetallic Strip Application

The heat generated by the current passing through the steel and brass strips raises their temperature, causing uneven expansion.

 Radiator Overflow Reservoir

bcoolant = 410 x 10-6 C-1            bradiator = 51  x 10-6 C-1

Radiator is full (15 quarts) when T = 6 C. How much overflow will occur at T = 92 C ? ----------------------------------------------------------- D T = 92 - 6 = 86 C Coolant:   D V = bV0 D T                         = (410 x 10-6 )(15)(86)                         = 0.529 quart  Radiator:  D V = bV0 D T                          = (51 x 10-6)(15)(86)                          = 0.066 quart  Overflow:  0.529 - 0.066 = 0.463 quart

   Ice is Less Dense than Water

Water molecules in crystal form have an open-structured hexagonal arrangement, so water expands upon freezing (water becomes less dense). (From Conceptual Physics, by Paul G. Hewitt)

 Why Do Lakes Freeze on the Top First?

Freezing of Lakes         As air above lake cools, the water at the top contracts and becomes more dense than the water below.  This cooler water sinks and warmer water takes its place at the top. When the lake is at 4 C, further lowering of the air temperature causes an expansion of the water on top.  This top water is now less dense than the water below, so it stays on top, where it freezes.