Reflection on Thermodynamics and Heat Transfer

How can we determine the final temperature of two objects in thermal contact?

Object A, with heat capacity CA and initially at temperature TA, is placed in thermal contact with object B, with heat capacity CB and initially at temperature TB. If the heat capacities are independent of the temperature and no phase changes occur, what is the final temperature of both objects?

Answer:

The final temperature of two objects in thermal contact with no heat loss is given by the formula a) (CA×TA + CB×TB) / (CA + CB), which is derived from the conservation of energy.

Reflecting on the principles of thermodynamics and heat transfer, we can understand the process of determining the final temperature of two objects in thermal contact. When considering the scenario of object A and object B being brought into thermal contact, with their respective heat capacities and initial temperatures, we delve into the concept of energy conservation to find the equilibrium temperature.

Given that no heat is lost to the surroundings and no phase changes occur, the conservation of energy dictates that the amount of heat lost by the hotter object (CA×TA) will be equal to the heat gained by the cooler object (CB×TB). This balance of energy transfer leads us to the formula for calculating the final temperature:

Tfinal = (CA×TA + CB×TB) / (CA + CB)

This formula represents the equilibrium point where the two objects reach a common final temperature after thermal contact. It highlights the relationship between the heat capacities and initial temperatures of the objects in determining their final state.