Final answer:
The question pertains to the Physics concept of heat transfer, specifically within thermodynamics, as it deals with temperature differential equations during various phases such as cooling, baking, freezing, and heating.
Step-by-step explanation:
When examining temperature differential equations related to a cake being taken out of the oven, we're dealing with the concept of heat transfer. This is a topic within the field of Physics, specifically thermodynamics, which concerns itself with the principles governing the energy exchange in the form of heat between systems at different temperatures. Whether it's cooling, as the cake comes out of the oven and loses heat to its surroundings; baking, where the oven provides a constant source of heat to cook the cake; freezing, which involves removing heat to turn a liquid into a solid; or heating, where energy is added to increase the temperature of the object, these processes are governed by temperature differential equations.
In the specific heat equation, the letter 'c' represents the specific heat, which is the amount of heat per unit mass required to raise the temperature by one degree Celsius. When designing a baking pan to bake batter fastest, different materials' specific heat capacities influence the rate at which they can transfer heat to the batter, thereby affecting the cooking time.