Final answer:
The increase in the air's temperature in a foundry when metal solidifies relates to the concept of specific heat capacity in physics. The given values allow for the calculation of the amount of heat transferred and its effect on the temperature of the air.
Step-by-step explanation:
Understanding Heat Transfer in Solidification
When molten metals cool and solidify, heat is transferred to the surroundings, such as air in a foundry. This process can be analyzed using concepts of thermodynamics and specific heat capacity. The specific heat capacity of air is given in the question as 1000 J/kg K. The energy added to the air from the solidifying metal is 9,900,000 J, and the temperature increase of the air is 55K.
To understand this process, consider how specific heat capacity relates to the amount of heat energy absorbed or released during temperature changes. For instance, water has a relatively high specific heat, while metals typically have lower values, indicating that less energy is needed to change their temperatures.
The cast iron frying pan examples illustrate that the larger pan's greater mass leads to a higher heat capacity and, thus, requires more energy for the same temperature change. In context, the heating of the air in the foundry showcases how the energy from the solidifying metal increases the kinetic energy of the air molecules, resulting in a rise in temperature.