?For the reversible isothermal compression of a liquid for which ? and ? may be assumed

Chapter 6, Problem 6.86

(choose chapter or problem)

For the reversible isothermal compression of a liquid for which β and κ may be assumed independent of pressure, show that:

(a) \(W = P_{1}V_{1} − P_{2}V_{2} − \frac {V_{2} − V_{1}}{κ}\)

(b) \(ΔS = \frac {β}{κ} (V_{2} − V_{1})\)

(c) \(ΔH = \frac {1− βT}{κ} (V_{2} − V_{1})\)

Do not assume that V is constant at an average value, but use Eq. (3.6) for its P dependence (with \(V_{2}\) replaced by V). Apply these equations to the conditions stated in Prob. 6.9. What do the results suggest with respect to use of an average value for V?

Text Transcription:

W = P_1V_1 − P_2V_2 − V_2 − V_1 / κ

ΔS = β / κ (V_2 − V_1)

ΔH = 1− βT/κ (V_2 − V_1)

V_2