The diagram illustrates a coffee thermos modeled as a lumped thermal system. The task is to derive the symbolic expression for the temperature change rate of the coffee, denoted as \( \frac{dT}{dt} \).### Diagram Explanation- **Thermos:** - **Thickness (L):** The thickness of the thermos walls. - **Surface Area (A):** The total surface area through which heat transfer occurs. - **Conductivity (k):** The thermal conductivity of the thermos material, which indicates how well it can conduct heat. - **Connectivity with Air (\( h_2 \)):** The convective heat transfer coefficient between the thermos surface and the surrounding air.- **Coffee:** - **Temperature (T):** The temperature of the coffee inside the thermos. - **Thermal Capacitance (C):** The heat capacity of the coffee, which determines how much heat is needed to change its temperature. - **Connectivity with the Thermos (\( h_1 \)):** The convective heat transfer coefficient between the coffee and the inner surface of the thermos.- **Ambient Temperature (\( T_a \)):** The temperature of the surrounding environment outside the thermos.This system describes how heat transfer affects the temperature of the coffee inside the thermos over time, taking into account the properties of the thermos and environmental conditions.

Answered: Image /qna-images/answer/c3aeb602-5c9b-4196-b844-384dfda6ef25.jpgCalculation of overall heat transfer coefficientThe value of U is calculated from systemThe system acts as lumped thermal systemBalancing the energy The rate of temperature change for coffee is .