Chapter 6, Problem 6.62P

Interpretation Introduction

Interpretation :

The maximum fraction of heat added to water in the boiler should be calculated that can be converted into work if it is vaporized and producing saturated vapor at given system and surrounding conditions. The statement about rest of heat during the process should be explained. The entropy change in the surroundings as result of work producing in system and total should be calculated.

Concept Introduction :

For the maximum fraction of heat added to water, we need to calculate maximum work from steam which is calculated at ideal hypothetical conditions. So, we use ideal work for the calculation of maximum fraction of heat added. The maximum fraction for the maximum work obtainable is calculated as:

  $\text{fraction=}\frac{\left|W_{ideal}\right|}{Q_{given}}$

Where $W_{ideal}=\stackrel{•}{m}\left(\Delta H-T_{\sigma }\Delta S\right)$

Since it is given that initially water is liquid at initial conditions hence, we use entropy and enthalpy equations for liquids which are:

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

  $dS=C_P\frac{dT}{T}+\beta VdP$