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

   $$\Delta U = \cancelto{0}{Q} - W.$$ (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.

   

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.

   

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

   
   
   therefore

   $$\Delta U = 0$$

   
   
   and

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