Question

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. The combination is thermally isolated each of equal mass. If the heat capacities are independent of the temperature and no phase changes occur, the final temperature of both objects is:

A) (CA * TA + CB * TB) / (CA + CB)
B) (CA * TA - CB * TB) / (CA - CB)
C) (CA * TA * CB * TB) / (CA * TB + CB * TA)
D) (CA + CB) / (TA + TB)

Answer 1

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.

Step-by-step explanation:

When 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, and no phase changes occur, the final temperature Tfinal of both objects can be found using the principle of conservation of energy.

Since there is no heat lost to the surroundings, the amount of heat lost by the hotter object will be equal to the heat gained by the cooler object. Therefore, the formula to calculate the final temperature is

Tfinal = (CA×TA + CB×TB) / (CA + CB), which corresponds to option A.