Chapter 6, Problem 6.86P

(a)

Interpretation Introduction

Interpretation:

Show that for the reversible isothermal compression of a liquid for which$\kappa$and$\beta$is assumed independent of pressure, work done is

  $W=P_1{V}_1-P_2{V}_2-\frac{V_2-V_1}{\kappa }$

Apply this equation on data used in Problem 6.9 to evaluate work done and comment on results obtain using an average value of$V$in Problem 6.9 and those using this equation

Concept Introduction:

The given equation is used whenever isothermal compressibility and volume expansivity are given and best in use for properties calculations.

  $\ln \frac{V_2}{V_1}=\beta \left(T_2-T_1\right)-\kappa \left(P_2-P_1\right)$

(b)

Interpretation Introduction

Interpretation:

Show that for the reversible isothermal compression of a liquid for which$\kappa$and$\beta$is assumed independent of pressure, entropy change is

  $\Delta S=\frac{\beta }{\kappa }\left(V_2-V_1\right)$

Apply this equation on data used in Problem 6.9 to evaluate entropy change and comment on results obtain using an average value of$V$in Problem 6.9 and those using this equation

Concept Introduction:

For liquids the entropy change is calculated as:

  $dS=C_P\frac{dT}{T}-\beta VdP$

(c)

Interpretation Introduction

Interpretation:

Show that for the reversible isothermal compression of a liquid for which$\kappa$and$\beta$is assumed independent of pressure, enthalpy change is

  $\Delta H=\frac{1-\beta T}{\kappa }\left(V_1-V_2\right)$

Apply this equation on data used in Problem 6.9 to evaluate enthalpy change and comment on results obtain using an average value of$V$in Problem 6.9 and those using this equation

Concept Introduction:

For liquids the enthalpy change is calculated as:

  $dH=C_{P}dT+\left(1-\beta T\right)VdP$