# When to use specific heat ($C_p$), and when to use enthalpy ($h$) to analyze steady flow

As I understand it, both enthalpy ($$h$$) and the specific heat at constant pressure ($$C_P$$) are intended to be used to study processes occurring at a constant pressure. Let $$m'$$ be mass flow rate, $$q$$ heat rate (power) $$C_P$$ be specific heat, $$h$$ be enthalpy and $$T$$ be temperature. Suppose I have a steady flow at constant pressure through a heat exchanger, and a temperature difference across that heat exchanger. How do I choose between using the enthalpy via $$q=m'(h_2-h_1)$$ and specific heat via $$q=m'{C_p}(T_2-T_1)$$ to analyze this flow.

How do I choose between using the enthalpy via $$q=m'(h_2-h_1)$$ and specific heat via $$q=m'{C_p}(T_2-T_1)$$ to analyze this flow.
$$h_{2}-h_{1}=c_{p}(T_{2}-T_{1})$$
But if the heat exchanger is a steam condenser or evaporator it is more convenient to calculate $$\dot q$$ using the enthalpies of the heat exchanger fluid than to use the temperature change of the fluid transferring heat with the exchanger. That's because the specific enthalpies of saturated steam are given in the saturated steam tables. Moreover, $$C_p$$ of the fluid transferring heat with the exchanger may vary slightly as a function of temperature.
The open system (control volume) version of the first law of thermodynamics applied to this problem tells us that the rate of heat addition to a stream passing through the heat exchanger is equal to the mass flow rate times the change in specific enthalpy of the stream. For a fluid at constant pressure, the specific enthalpy change is $$\Delta h=C_p\Delta T$$ (assuming constant heat capacity). So, if you want to find the change in temperature, you have to express $$\Delta h$$ in terms of the temperature. For non-constant pressure of an incompressible fluid, $$\Delta h=C_p\Delta T+v\Delta P$$, although the 2nd term is usually negligible.