Question

What is the relation \(h_{\text {heat }}=\rho c_{p} h_{\text {mass }}\) known as? For what kind of mixtures is it valid? What is the practical importance of it?

Short answer

Answer: The Sensible Heating Equation is given by \(h_{\text{heat}} = \rho c_p h_{\text{mass}}\), which represents the heat transfer in a process where only the temperature of a substance changes, and no phase change occurs. It has practical importance in various fields, such as designing and optimizing heating systems, calculating energy requirements, and understanding and controlling thermal processes. This equation is mainly applicable for ideal gas mixtures and some liquid mixtures with constant heat capacity over the temperature range of interest.

Step-by-step solution

Identify the relation

The given relation \(h_{\text{heat}} = \rho c_p h_{\text{mass}}\) is known as Sensible Heating Equation. It represents the heat transfer process in which only the temperature of the substance changes, and no phase change takes place. In this equation: - \(h_{\text{heat}}\) is the heat transfer per unit volume - \(\rho\) is the density of the material - \(c_p\) is the specific heat capacity of the material at constant pressure - \(h_{\text{mass}}\) is the enthalpy increase per unit mass

Determine for which mixtures it's valid

The Sensible Heating Equation is valid for mixtures that have uniform and stable properties, and where the heat capacity is constant over the temperature range of interest. Examples of such mixtures include ideal gas mixtures and some liquid mixtures. It is important to note that this equation may not be accurate for mixtures where properties change significantly with temperature, or where phase changes (like boiling, melting, or evaporation) occur during the heating process.

Explain its practical importance

The Sensible Heating Equation has several practical applications, mainly in the fields of engineering, physics, and chemistry. Some of its uses include: 1. Designing and optimizing heating systems: By understanding how heat transfer depends on the material properties and temperature changes, engineers can design more energy-efficient heating systems and improve existing ones. 2. Calculating energy requirements: The equation helps in estimating the amount of energy needed to raise the temperature of a material, which is crucial in various industrial processes such as metal casting, food processing, and heat treatment of materials. 3. Understanding and controlling thermal processes: A good grasp of this relationship allows scientists and engineers to better control and manage thermal processes, thus ensuring the desired outcome is achieved. Overall, the Sensible Heating Equation is important as it provides a fundamental basis for understanding heat transfer in a range of practical situations.