Question 2.12: Using data from the steam tables in Appendix A, estimate the...

There is no entry in the steam tables at 350 kPa (3.5 bar). Interpolation between the data at 3 and 4 bar, and 200 ˚C, can be used to find the specific enthalpy at 3.5 bar and 200 ˚C. But what we actually seek is the change in specific enthalpy, so we will instead look at the temperatures above and below 200 ˚C.

Steam at 350 kPa and 150°C →Interpolation Needed Interpolate

Steam at 350 kPa and 250°C → Interpolation Needed Interpolate

Constant pressure heat capacity \left(\mathrm{C}_{\mathrm{P}}\right) can be estimated as

\mathrm{C}_{\mathrm{P}} \approx \frac{\Delta \mathrm{H}}{\Delta \mathrm{T}}=\frac{2966.2 \frac{\mathrm{kJ}}{\mathrm{kg}}-2757.0 \frac{\mathrm{kJ}}{\mathrm{kg}}}{250^{\circ} \mathrm{C}-150^{\circ} \mathrm{C}}=2.092 \frac{\mathrm{kJ}}{\mathrm{kg}^{\circ} \mathrm{C}}

If we attempt to apply a directly analogous procedure at 700 kPa (7 bar) there is a complication:

Water at 700 kPa and 150°C →Liquid
Since these two intensive properties do not yield a vapor, we must use the enthalpy of saturated vapor at 700 kPa. This temperature is 164.9°C

Steam at 700 kPa and 164.9°C → 2762.8 \frac{\mathrm{kJ}}{\mathrm{kg}}

Steam at 700 kPa and 250°C → Interpolation Needed
Interpolate

These answers are fairly similar, but different enough to demonstrate that \mathrm{C}_{\mathrm{P}} can in reality be a function of pressure as well as temperature. This is why the distinction between “ideal gas heat capacity” and simply “heat capacity” is important; ideal gas heat capacity is only a function of temperature.

Conceptually, we could get more accurate estimates of C_{P} by using values of \widehat{H} that were closer to the actual temperature of interest; e.g., 190 and 210°C instead of 150 and 250°C. But that data is not included in the available version of the steam table.