A 0.5 kg metal block at 100°C with a specific heat of 400 J/kg·K is placed in 1.0 kg of water at 20°C with a specific heat of 4200 J/kg·K. What is the final temperature?

The problem describes a calorimetry scenario where a hot metal block is placed into cooler water. We assume that the heat lost by the metal block is equal to the heat gained by the water, and no heat is lost to the surroundings.

Given values:

• Mass of metal block, $m_m = 0.5 \text{ kg}$
• Initial temperature of metal block, $T_{m,i} = 100^\circ\text{C}$
• Specific heat capacity of metal, $c_m = 400 \text{ J kg}^{-1} \text{ K}^{-1}$
• Mass of water, $m_w = 1.0 \text{ kg}$
• Initial temperature of water, $T_{w,i} = 20^\circ\text{C}$
• Specific heat capacity of water, $c_w = 4200 \text{ J kg}^{-1} \text{ K}^{-1}$

Let the final temperature of the mixture be $T_f$.