One mole of an ideal gas with = (7/2)R and = (5/2)R expands from = 8 bar and = 600 K to = 1 bar by each of the following paths:

Question

What will be an ideal response?
(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

a. Constant volume expansion from 8 bar and 600 K to 1 bar. Since PV/T is constant for an ideal gas, when P decreases by a factor of 8, T will also decrease by a factor of 8 to maintain constant volume, so in this case the final temperature is 600/8 = 75 K. As for any constant volume process, the work done is zero (W = 0). The heat transfer required is



The change in internal energy is ?U = Q = -10910 J

The change in enthalpy is



b. For isothermal expansion, we know that ?H = ?U = 0.

The heat flow required is



The work done is



c. For adiabatic expansion, we have



So we have = 0.5520*600 K = 331 K

Then

And

By definition, Q = 0.

Finally, W = ?U = -5591.50 J

On a PV diagram, the three paths look like this: