Thermal Energy Physics Example 2

Solution

1. 1
   Heat lost by iron = heat gained by water: $m_{\text{Fe}} c_{\text{Fe}} (T_i^{\text{Fe}} - T_f) = m_w c_w (T_f - T_i^w)$.
2. 2
   $$0.5 \times 450 \times (200 - T_f) = 2 \times 4186 \times (T_f - 20)$$
3. 3
   $$225(200 - T_f) = 8372(T_f - 20) \implies 45000 - 225T_f = 8372T_f - 167440$$
4. 4
   $$212440 = 8597T_f \implies T_f \approx 24.7°\text{C}$$