Summary: Physics 408 -- Exam 1 Name So)w-;o11
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 C, at constant
volume and C,, at constant pressure, and with y C I .C, . 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
(b) (4) Using the first law, obtain the relation between C,,, dE, and dT.
V fid -e
·= E = C T