Question

Determine the final temperature when two bodies at different temperatures are brought into thermal contact.

• A. The temperature will always be the average of the two temperatures.
• B. The temperature will depend on the masses and specific heats of the bodies.
• C. The temperature will always be the temperature of the body with the higher initial temperature.
• D. The temperature will be the higher of the two initial temperatures.

Hint:

To find the final temperature of two bodies in thermal contact, use the equation \( T_f = \frac{m_1 c_1 T_1 + m_2 c_2 T_2}{m_1 c_1 + m_2 c_2} \), which accounts for the masses and specific heats.

Answer 1

The Correct Option is B

This problem involves the concept of thermal equilibrium and the principle of heat exchange.
1. Heat Transfer and Energy Conservation: - When two bodies at different temperatures come into thermal contact, heat flows from the hotter body to the cooler body until both bodies reach the same final temperature. This process is governed by the first law of thermodynamics, which is essentially the law of conservation of energy.
2. The amount of heat \( Q \) transferred is given by: \[ Q = mc \Delta T \] Where: - \( m \) is the mass of the body, - \( c \) is the specific heat capacity of the material, - \( \Delta T \) is the change in temperature (\( T_f - T_i \)). 3. Equation Setup: - Let the masses of the two bodies be \( m_1 \) and \( m_2 \), their specific heats be \( c_1 \) and \( c_2 \), and their initial temperatures be \( T_1 \) and \( T_2 \), respectively. - The heat lost by the hotter body equals the heat gained by the cooler body. This can be written as: \[ m_1 c_1 (T_f - T_1) = - m_2 c_2 (T_f - T_2) \] Where \( T_f \) is the final temperature that we need to solve for. 4. Solving for Final Temperature: - Rearranging the equation: \[ m_1 c_1 (T_f - T_1) = - m_2 c_2 (T_f - T_2) \] \[ m_1 c_1 T_f - m_1 c_1 T_1 = - m_2 c_2 T_f + m_2 c_2 T_2 \] \[ (m_1 c_1 + m_2 c_2) T_f = m_1 c_1 T_1 + m_2 c_2 T_2 \] \[ T_f = \frac{m_1 c_1 T_1 + m_2 c_2 T_2}{m_1 c_1 + m_2 c_2} \] 5. This equation shows that the final temperature depends on the masses and specific heat capacities of the bodies involved. Option (1) is incorrect because it assumes the final temperature is just the average of the initial temperatures. Option (3) and (4) are incorrect because they ignore the relationship between mass, specific heat, and energy transfer.
Option (2) is correct.