Energy and Entropy: Fall-2020
Practice midterm (not graded): Due Friday 10/23

  1. Midterm practice
    Consider the pictured insulated piston, which is initially in thermal and mechanical equilibrium. The piston contains an unknown fluid. You add some masses to the top of the piston.
    1. Does the pressure on the fluid increase, decrease, or remain the same, or can you not tell? Why?

    2. Does the entropy of the fluid increase, decrease, or remain the same, or can you not tell? Why?

    3. Does the internal energy of the fluid increase, decrease, or remain the same, or can you not tell? Why?
    Note that an erroneous "cannot tell" will score higher than an incorrect prediction.
  2. Midterm practice Consider the following equations for internal energy and identify any problems that might indicate that they are erroneous. If the equation must be incorrect, please identify why it must be incorrect.
    1. \(U = p S + \frac32 Nk_BT\)
    2. \(U = \frac52 p V\)
    3. \(U = \frac32Nk_BT\ln\left(1+N\right)\)
  3. Midterm practice Find \(\left(\frac{\partial m}{\partial h}\right)_g\) given the equations below. Show your work. \begin{align} m &= f^2 \sin(3h+g^2)\\ g &= fh \end{align}
  4. Midterm practice Consider the variable \(F\) in \begin{align} F = U - TS \end{align} where \(U\) is the internal energy, \(T\) is the temperature, and \(S\) is the entropy. Solve for the partial derivative \(\left(\frac{\partial F}{\partial T}\right)_V\) where \(V\) is the volume.