One mole of an ideal gas with expands from and to bar by each of the following paths:

Question

(a) Constant volume
(b) Constant temperature
(c) Adiabatically
Assuming mechanical reversibility, calculate W, Q, ?U, and ?H for each process. Sketch each path on a single PV diagram.

Answer 1

For each of these problems start with equations 3.13b, 3.14b, 3.16, and 3.17:



(a) at constant volume,



So plugging the given values into each part gives:





Now not knowing what T2 is, we must assume to stay at an ideal gas that since the pressure drops by a factor of 6, the temperature must drop by the same as well, leaving T2 = 800/6 = 133.33 K. Using this value gives the following values:





(b) Using the same starting point as in part (a) and assuming constant temperature, reduces the equations to the following:





Putting in the known values and solving gives





(c) Again starting with the same equations as in part (a) and assume dQ = 0 (adiabatic) gives:





However, we also have adiabatic expansion which changes T2. Taking Eqn 3.16 integrating and solving for T2 gives:





Plugging in given values and solving gives: