Question 2.17: A) Using the steam tables, find the change in specific entha...

A) Water at 10 bar and 80^{\circ} \mathrm{C} \rightarrow 335.77 \frac{\mathrm{kJ}}{\mathrm{kg}}

Saturated vapor at 10 \mathrm{bar} \rightarrow 2777.11 \frac{\mathrm{kJ}}{\mathrm{kg}}

\begin{aligned}&\Delta \widehat{\mathrm{H}}=\widehat{\mathrm{H}}_{\mathrm{out}}-\widehat{\mathrm{H}}_{\mathrm{in}}\\&2777.11 \frac{\mathrm{kJ}}{\mathrm{kg}}-335.77 \frac{\mathrm{kJ}}{\mathrm{kg}}=\mathbf{2 4 4 1 . 3 4} \frac{\mathbf{k J}}{\mathbf{k g}}\end{aligned}

B) The boiling point of water at 10 bar, according to the steam tables, is 179.88°C, or 453 K. Thus, the increase in temperature (ΔT) is almost exactly 100°C.

C) There is a large difference between the answers to A and B. The value found through the steam tables is the change in specific enthalpy from 80°C liquid that has been heated to its boiling point (at 10 bar) and then converted to a vapor. This extra heat added to convert a liquid to a vapor is very significant. In part b), we ignored this step—the final state was liquid water at its boiling point (at 10 bar).

We must always remember, the expression \mathrm{d} \underline{\mathrm{H}}=\mathrm{C}_{\mathrm{P}} \mathrm{dT}, or \mathrm{d} \widehat{\mathrm{H}}=\hat{C}_{P} \mathrm{dT}, is valid when a temperature change is the only thing occurring in a process-it does not account for changes in pressure or changes in phase.