Final answer:
The object you're describing is a double boiler, used for gentle cooking. In terms of physics, larger frying pans require more energy to heat up due to their larger heat capacity, but if made from the same material, they would have the same specific heat.
Step-by-step explanation:
You seem to be describing a double boiler or bain-marie, which is a kitchen tool used to cook foods gently, often used for melting chocolate or cooking custards without scorching them. Regarding the physics of cooking utensils like frying pans, the heat capacity of an object is the amount of heat energy required to raise its temperature by a certain amount. This is why a larger frying pan, like a cast iron pan, has a larger heat capacity compared to a smaller pan. When they are made of the same material, they would have the same specific heat, which is the amount of heat per unit mass required to raise the temperature by one degree Celsius.
The larger pan in your example requires 90,700 Joules (J) to raise its temperature by 50.0 °C, indicating it has a larger mass and hence a larger heat capacity. This corresponds with the concept that objects with larger mass and same material require more energy for the same temperature change, because specific heat is a property that only depends on the material, not the mass or volume of the object.