Summary: Physics 408 -- Exam 1 Name_______________________________________
You are graded on your work, with partial credit where it is deserved.
Please give clear, well-organized solutions, and please show enough work to be convincing.
1. We will consider the vibrations of a cylinder with cross-sectional area A
and mass m , floating above an ideal gas with heat capacity CV at constant
volume and CP at constant pressure, and with ! " CP / CV . No energy
leaves or enters the gas, so the vibrations are adiabatic.
You may assume the ideal gas equation of state PV = NkT , and the fact
that E = E T( ) for an ideal gas.
But please do not assume other properties, such as the relation between
V and P or T during an adiabatic process, since these are equivalent to
some of what is asked for below.
(a) (4) Write down the first law of thermodynamics, relating the change in
internal energy dE to the heat dQ added to the gas and the work dW done
by the gas*.
(b) (4) Using the first law, obtain the relation between CV , dE , and dT .
(c) (4) Using the first law, plus the ideal gas equation of state, show that CP ! CV = constant , and obtain the
constant in terms of the number of particles N and the Boltzmann constant k .
* This is a slight change of notation, and with no explicit indication that Q and W are not proper variables.