[SOLVED] Phys 362 statistical and thermal physics: homework 3

The linear thermal expansion coefficient describes the increase in length of a homogenous
material as its temperature changes and is defined by
1 :=
1
L
L
T
where L is the length of the material.The subscript in 1 is not standard notation; it
is included to distinguish the linear thermal expansion coefficient from the volume thermal
expansion coefficient.a) For copper, 1 = 1.65105 K1. Determine the amount by which a copper rod of length
10 m will expand if it is heated from 10 C to 30 C, assuming that is independent
of temperature.b) A rectangular sheet of any material will expand as its temperature increases. Here the
coefficient of area expansion is defined by
:=
1
A
A
T
where A is the area of the material. Show that
= 21.Determine the amount by which the area of a rectangular copper roof, whose sides are
10 m and 4 m increases if it is heated from 10 C to 30 C.Determine an expression for the thermal expansion coefficient for a van der Waals gas. Hint:
note that differentiation of V w.r.t. T will be difficult. There is an identity that we encountered
in class that will make this easier.Determine an expression for the isothermal compressibility of an ideal gas, in terms of N,P
and T. Show that it is positive.The state of a solid material can be described by the same variables as for a gas. Suppose
that the equation of state of the solid is
V = V0 (1 + aT bP)
where V0 is a constant equal to the volume when pressure and temperature are zero and a
and b are constants that are very small.a) Determine expressions for the isothermal compressibility and the isobaric expansion
coefficient.b) Suppose that a and b are so small that at typical temperatures aT # 1 and bP # 1.
Determine approximate expressions for the isothermal compressibility and the isobaric
thermal expansion coefficient in this case. Are they approximately constant or not?