The specific heat capacity at constant pressure of steam at atmospheric pressure is given by $$ c_{P}=a+b T+c T^{2} $$ where \(a=1.912 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{deg}\) $$ \begin{aligned} &b=1.727 \times 10^{-3} \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{deg}^{2} \\ &c=-4.667 \times 10^{-6} \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{deg}^{3} \end{aligned} $$ If the specific enthalpy of saturated steam at \(100^{\circ} \mathrm{C}\) is \(2676 \mathrm{~kJ} / \mathrm{kg}\), what is the specific enthalpy of superheated steam at the same pressure and a temperature of \(300^{\circ} \mathrm{C} ?\)

Enthalpy is a measurement of total heat content in a system. When calculating enthalpy for steam, such as in our exercise, the process involves several important steps. First, you need the specific heat capacity expression, which will help to find the additional heat required to superheat the steam. Here, the specific heat capacity of steam at constant pressure is provided as a function of temperature:

• $$ c_{P} = a + b T + c T^{2} $$

By knowing the specific heat at a given temperature, we can determine the change in enthalpy using the formula:

• $$ ΔH = c_{P} \times ΔT $$

In the exercise, this formula and values were used to calculate the enthalpy for steam heated from 100°C to 300°C.

Specific heat capacity is the amount of heat required to raise the temperature of one kilogram of a substance by one degree Celsius. In the context of our exercise, the specific heat capacity of steam at constant pressure is expressed as:

• $$ c_{P} = a + b T + c T^{2} $$

The constants used in the equation are:

• $$a = 1.912 \text{ kJ/kg·°C}$$
• $$b = 1.727 \times 10^{-3} \text{ kJ/kg·°C²}$$
• $$c = -4.667 \times 10^{-6} \text{ kJ/kg·°C³}$$

These constants need to be substituted into the equation to determine the specific heat capacity at a particular temperature, such as 300°C.

In heat and thermodynamics, understanding concepts such as specific heat capacity and enthalpy is crucial. The specific heat capacity tells us how much heat energy is required to change the temperature of a substance. For thermodynamic processes involving steam, specific heat capacity and enthalpy calculations help engineers design systems like boilers and turbines efficiently. We must also consider that heat transfer into steam results in changing phases. In our exercise, it involves calculating the enthalpy of superheated steam, which means applying thermodynamic principles to determine the amount of energy added to the system. The formula and constants provided help in these calculations, connecting the change in temperature to the total heat added.

Superheated steam is steam that has been heated beyond its boiling point at a given pressure without any phase change (remaining as steam). This state of steam is significant in various industrial applications because it contains more energy and can do more work compared to saturated steam. In our exercise, we deal with calculating the specific enthalpy of superheated steam at 300°C. By using the specific heat capacity and the known enthalpy of steam at 100°C, we determined the additional heat content required to raise the temperature of the steam to 300°C. The result helps in understanding the properties and potential energy of superheated steam, which is essential for optimizing thermal systems and improving efficiency in processes like power generation.