# Is there any relation between the specific heat of steam and enthalpy?

I am trying to understand if there is any link between the specific heat of the steam and the enthalpy of saturated vapor.

For instance, the specific heat of water in liquid state at $20^{\circ}C$ is:

$C_p = 4.18 kJ/kg/K$ for Liquid Water

But the steam, at the same temperature is way lower

$C_p = 1.87 kJ/kg/K$ for Steam

1. Why is the specific heat of steam lower?

2. Is there any ways I can calculate the specific heat for the steam by using the saturation enthalpies?

At $20^{\circ}C$ the enthalpy of saturated liquid is: $h_f = 83.915 kJ/kg$ and the enthalpy of saturated vapor is: $h_g = 2537.4 kJ/kg$ and the vaporization enthalpy $h_{vap} = 2453.485 kJ/kg$

I can easily get those values by using $h_f = C_pT$ and $h_g = C_pT + h_{vap}$ as seen here.

How can one obtain the specific heat for the Steam? Is there any way to get that 1.87 kJ/kg/K value?

Thank you!

The specific heat of a substance at constant pressure is defined as follows:$$C_p=\left(\frac{\partial h}{\partial T}\right)_p$$ So, to get the specific heat of steam at saturation (or above saturation, in the superheated region), you need to use the tables for superheated steam at constant pressure, and numerically differentiate the enthalpy with repsect to temperature.