Final answer:
The object with the least mass (100g) will heat up faster than the object with the most mass (200g) because it requires less energy to increase its temperature given the specific heat capacity is constant. This is based on the concept of specific heat capacity and thermal properties in physics.
Step-by-step explanation:
The question you're asking is about thermal properties and how they relate to mass. Objects with differing masses will absorb and transfer heat energy at different rates due to their mass and specific heat capacity. Specifically, if two objects are made of the same material and are exposed to the same heat source, the object with the least mass (100g in this case) will heat up faster than the object with the most mass (200g). This is because the specific heat capacity is a measure of how much energy is needed to raise the temperature of a certain mass of a substance by a certain temperature. Therefore, with less mass to heat, the smaller object reaches a higher temperature quicker.
Regarding the other problems you mentioned, such as the heating of different materials or mixing substances at different temperatures, they all involve the principles of thermodynamics and heat transfer. For instance, when two substances at different temperatures are mixed in a calorimeter, the amount of heat lost by the warmer substance will be gained by the colder one until they reach thermal equilibrium. The final temperature and state of the substances depend on their masses, specific heat capacities, and the phase changes that might occur during the process.