Integrating into the superheated region

While for an ideal gas, Cp will have a constant value, Cp for superheated steam will depend on both temperature and pressure. We will assume that it is possible to fix an average value of specific heat for steam at each pressure that takes into account the sometimes substantial variations with temperature over the path of integration. Hence equation (16.59) becomes 

Meanwhile, we may also integrate equation (16.38) with respect to temperature from saturation conditions under the assumption that the specific heat is independent of temperature. This gives  

It will be noted that these conversion equations depend on a temperature-invariant, average specific heat of steam at constant pressure, and such a figure will apply only at one temperature in the superheat region. Fortunately the specific heat terms in each equation undergo 

Let us assume that our estimate of average specific heat over the integration path contains an error, e, so that Cp- Cp + e. Making use of the exponential expansion  

Since for steam turbine operation we may assume Cp 2000 J/(kg K) and s - Sg 2000 J/(kg K), squared and higher terms in (16.66) will contribute relatively little to the final figure, and may be neglected for the purpose of estimating the effect of the error in specific heat on the calculation of specific enthalpy. Assuming the error in average specific heat is fractional, we may expand using the binomial expansion  

---