Burt Rutan's White Knight and SpaceShip One, Photo Courtesy of Scaled Composites
Thermodynamics and Propulsion

2.2 Corollaries of the First Law

  1. Work done in any adiabatic ($ Q=0$ ) process is a function of state. We can write the first law, setting the heat transfer term equal to zero, as

    $\displaystyle \Delta U = \cancelto{0}{Q} - W.$ (2..3)

    Since $ \Delta U$ depends only on the state change, now $ W$ can be found as a function of the state change.

    Figure 2.3: The change in energy between two states is not path dependent.
    Image fig3AdiabaticWorkPathIndependence_web

  2. For a cyclic process heat and work transfers are numerically equal

    Figure 2.4: Since energy is a function of state only, any process that returns a system to its original state leaves its energy unchanged.
    Image fig3CyclicPathWEqualsQ_web

    $\displaystyle U_{\textrm{final}} = U_{\textrm{initial}}$    


    $\displaystyle \Delta U = 0$    


    $\displaystyle Q = W \qquad \textrm{or}\qquad \oint \delta Q=\oint \delta W$