The specific enthalpy of liquid n-hexane at 1 atm varies linearly with temperature and

Chapter 7, Problem 7.23

(choose chapter or problem)

The specific enthalpy of liquid n-hexane at 1 atm varies linearly with temperature and equals 25.8 kJ/kg at \(30^{\circ} \mathrm{C}\) and 129.8 kJ/kg at \(50^{\circ} \mathrm{C}\).

(a) Determine the equation that relates \(\hat{H}(\mathrm{~kJ} / \mathrm{kg}) \text { to } T\left({ }^{\circ} \mathrm{C}\right)\) and calculate the reference temperature on which the given enthalpies are based. Then derive an equation for \(\hat{U}(T)(\mathrm{kJ} / \mathrm{kg})\) at 1 atm.

(b) Calculate the heat transfer rate required to cool liquid n-hexane flowing at a rate of 20 kg/min from \(60^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C}\) at a constant pressure of 1 atm. Estimate the change in specific internal energy (kJ/kg) as the n-hexane is cooled at the given conditions.