Final answer:
The question involves understanding thermal equilibrium and heat transfer, which are part of Physics, but cannot be answered accurately without further context or information on initial conditions and material properties.
Step-by-step explanation:
The question relates to the concept of thermal equilibrium and heat transfer, which are key topics in Physics. The temperature difference mentioned cannot be determined without additional information, such as the initial temperature and the thermal properties of the cup. However, the information provided depicts several scenarios involving thermal interactions between different materials and quantities of water with the surrounding environment or with other objects. In each case, the final temperature after heat exchange is what is being calculated or inferred.
For instance, in the case of the aluminum spoon and the coffee, the concept of specific heat capacity is used to determine the final temperature in thermal equilibrium. Similarly, the melting of ice in a calorimeter and finding the temperature at which both water and a pan reach thermal equilibrium employ the principles of calorimetry and thermal conductivity.