104 g of water at 30°C is taken in a calorimeter made of copper of mass 42 g

Heat (10)

104 g of water at 30°C is taken in a calorimeter made of copper of mass 42 g. When a certain mass of ice at 0°C is added to it, the final steady temperature of the mixture after the ice has melted, was found to be 10°C. Find the mass of ice added. [Specific heat capacity of water = 4.2 Jg^-1°C^-1; Specific latent heat of fusion of ice = 336 Jg^-1; Specific heat capacity of copper = 0.4 Jg^-1°C^-1]

Answer

By principle of mixtures

m_iceL + m_ice c_w t = m_w c_w (t_i - t_f) + m_cu c_cu (t_i - t_f)

m (336 + 4.2 × 10) = 104 × 4.2 × (30 - 10) + 42 × 0.4 × (30 - 10)

m × 4.2 (80 + 10) = 4.2 × (104 + 4) × 20

m = (108 × 20)/90 = 24 g