Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 67

In the extrusion of cold chocolate from a tube, work is done on the chocolate by the pressure applied by a ram forcing the chocolate through the tube. The work per unit mass of extruded chocolate is equal to \(p/\rho\), where \(p\) is the difference between the applied pressure and the pressure where the chocolate emerges from the tube, and \(\rho\) is the density of the chocolate. Rather than increasing the temperature of the chocolate, this work melts cocoa fats in the chocolate. These fats have a heat of fusion of \(150 \text{ kJ/kg}\). Assume that all of the work goes into that melting and that these fats make up \(30\%\) of the chocolate's mass. What percentage of the fats melt during the extrusion if \(p = 5.5 \text{ MPa}\) and \(\rho = 1200 \text{ kg/m}^3\)?