A calorimeter contains 50 g of water at 50°C. The temperature falls to 45°C in 10 minutes. When the calorimeter contains 100 g of water at 50°C. it takes 18 minutes for the temperature to become 45°C. Find the water equivalent of the calorimeter.

Sol. Let the water eq. of calorimeter = m (m + 50 * 10^-3) * 4200 * 5/10 = Rate of heat flow (m + 100 * 10^-3) * 4200 * 5/18 = Rate of flow ⇒ (m + 50 * 10^-3) * 4200 * 5/10 = (m + 100 * 10^-3) * 4200 * 5/18 ⇒ (m + 50 * 10^-3) 18 = 10m + 100 * 10^-3 ⇒ 18m + 18 * 50 * 10^-3 = 10m + 1000 * 10^-3 ⇒ 8m = 100 * 10^-3 kg ⇒ m = 12.5 * 10^-3 kg = 12.5 g