The internal energy is of any ideal gas can be written as
U &= U(T,N)
meaning that the internal energy depends only on the number of
particles and the temperature, but not the volume.* The ideal gas law
pV &= Nk_BT
defines the relationship between \(p\), \(V\) and \(T\). You may take the
number of molecules \(N\) to be constant. Consider the free adiabatic
expansion of an ideal gas to twice its volume. “Free expansion”
means that no work is done, but also that the process is also
neither quasistatic nor reversible.
What is the change in entropy of the gas? How do you know
- What is the change in temperature of the gas?