0.5kg of water at 10oC is completely converted to ice by extracting 188000J of heat from it. If the specific heat capacity of water is 4200J kg-1C-1, calcul...

The specific latent heat of fusion of ice is the amount of energy required to change the state of a unit mass of ice from solid to liquid or from liquid to solid without changing its temperature. We can calculate the specific latent heat of fusion of ice by using the formula: Q = mL where Q is the amount of energy transferred, m is the mass of the substance, and L is the specific latent heat of fusion. In this case, we know that 0.5kg of water at 10°C is completely converted to ice by extracting 188000J of heat from it. We also know that the specific heat capacity of water is 4200J kg^-1C^-1. First, we need to calculate the amount of energy required to cool the water from 10°C to 0°C: Q1 = mcΔT where m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. Q1 = (0.5kg)(4200J kg^-1C^-1)(10°C) = 21000J Next, we need to calculate the amount of energy required to convert the water at 0°C to ice at 0°C: Q2 = mL where m is the mass of water, and L is the specific latent heat of fusion of ice. Q2 = (0.5kg)(L) We know that the total amount of energy transferred is 188000J. Therefore, we can write: Q1 + Q2 = 188000J Substituting the values of Q1 and Q2, we get: 21000J + (0.5kg)(L) = 188000J Simplifying and solving for L, we get: L = (188000J - 21000J) / 0.5kg L = 334000J kg^-1 Therefore, the specific latent heat of fusion of ice is 334.0 KJ kg^-1. So the answer is: - 334.0 KJ kg^-1.