This problem addresses thermal equilibrium and heat exchange principles.
1. Heat Transfer and Energy Conservation:
- Heat transfers from a hotter to a cooler body upon thermal contact until thermal equilibrium is reached (equal final temperature). This aligns with the first law of thermodynamics (conservation of energy).
2. Heat Transferred \( Q \):
\[
Q = mc \Delta T
\]
- \( m \): mass of the body
- \( c \): specific heat capacity
- \( \Delta T \): temperature change (\( T_f - T_i \))
3. Equation Formulation:
- For two bodies with masses \( m_1, m_2 \), specific heats \( c_1, c_2 \), and initial temperatures \( T_1, T_2 \):
- Heat lost by hotter body = Heat gained by cooler body.
\[
m_1 c_1 (T_f - T_1) = - m_2 c_2 (T_f - T_2)
\]
- \( T_f \) is the final equilibrium temperature.
4. Final Temperature Calculation:
- 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. The final temperature is determined by the masses and specific heat capacities of the bodies. Option (1) is incorrect as it simplifies the final temperature to a mere average of initial temperatures. Options (3) and (4) are flawed for disregarding the relationship between mass, specific heat, and energy transfer. Option (2) is correct.