# Chapter 2 : Expansion¶

## Example 2.1 Page No : 24¶

In [1]:
# Input data
l = 1.  # The thickness of the crystal in cm
w = 5890. - 8  # The wavelength of light used in cm
t2 = 50.  # The final temperature of the crystal in degree centigrade
t1 = 20.  # The initial temperature of the crystal in degree centigrade
p = 14.  # The number of fringes that crossed the field of view

# Calculations
t = t2 - t1  # The temperature difference in degree centigrade
# The coefficient of linear expansion of the crystal in per degree centigrade
a = (p * w) / (2 * l * t)

# output
print 'The coefficient of linear expansion of the crystal is %3.4g degree centigrade' % (a)

The coefficient of linear expansion of the crystal is 1372 degree centigrade


## Example 2.2 Page No : 31¶

In [2]:
# Input data
L = 500.  # The length of a steel rod in cm
t = 40.  # The increase in temperature in degree centigrade
y = 2. * 10**12  # The youngs modulus of elasticity of steel in dynes/cm**2
e = 12. * 10**-6  # The coefficient of linear expansion of steel in per degree centigrade

# Calculations
S = y * e * t  # The stress in the rod in dynes/cm**2

# Output
print 'The stress in the rod is %3g dynes/cm^2' % (S)

The stress in the rod is 9.6e+08 dynes/cm^2


## Example 2.3 Page No : 36¶

In [3]:
# Input data
L = 800.  # The length of the wire in cm
r = 0.2  # The radius of the wire in cm
t = 10.  # The temperature fall in degree centigrade
a = 12. * 10**-6  # The coefficient of linear expansion of steel wire in per degree centigrade
y = 2. * 10**12  # The youngs modulus of elasticity of steel in dynes/cm**2
pi = (22. / 7)  # Mathematical constant pi

# Calculations
I = y * a * t * pi * r**2  # The increase in tension in dynes

# Output
print 'The increase in tension is %3g dynes' % (I)

The increase in tension is 3.01714e+07 dynes


## Example 2.4 Page No : 39¶

In [5]:
# Input data
A = 2. * 10**-6  # The cross section area of a uniform rod in m**2
t = 20.  # The change in temperature in degree centigrade
y = 10.**11  # The youngs modulus of the rod in newtons/m**2
a = 12. * 10**-6  # The coefficient of linear expansion of rod in per degree centigrade

# Calculations
F = y * a * t * A  # The force required to prevent it from expanding in newtons
E = (1. / 2) * y * a * t * a * t  # The energy stored per unit volume in j/m**3

# Output
print 'The force required to prevent the rod from expanding is %3.0f newtons  \
\nThe Energy stored per unit volume is %3.0f j/m^3' % (F, E)

The force required to prevent the rod from expanding is  48 newtons
The Energy stored per unit volume is 2880 j/m^3


## Example 2.5 Page No : 41¶

In [6]:
# Input data
d = 10.**-3  # The diameter of a steel wire in m
t = 20.  # The difference in the temperature in degree centigrade
y = 2. * 10**11  # The youngs modulus of a steel wire in newtons/m**2
a = 12. * 10**-6  # The coefficient of linear expansion of steel wire in per degree centigrade
pi = (22. / 7)  # Mathematical constant value

# calculations
A = (pi * d**2) / 4  # The cross sectional area of the steel wire in m**2
# Force required to maintain the original length in kg wt
F = (y * a * t * A) / (9.8)

# output
print 'Force required to maintain the original length is %3.3f kg wt ' % (F)

Force required to maintain the original length is 3.848 kg wt