The quantity of heat energy required to melt completely 1 kg of ice at - 30oC is [latent heat of fusion = 3.5 x 10 5Jkg -1, specific heat capacity of ice = ...

When a substance changes its phase, it either absorbs or releases heat energy. The amount of heat energy required to change the phase of a substance is known as the latent heat of fusion. In this case, we have to calculate the quantity of heat energy required to melt completely 1 kg of ice at -30°C. To do this, we need to use the following formula: Q = m Lf Where Q is the quantity of heat energy, m is the mass of the substance, and Lf is the latent heat of fusion. We are given that the mass of the ice is 1 kg, and the latent heat of fusion of ice is 3.5 x 10^5 Jkg^-1. So, substituting these values into the formula, we get: Q = 1 kg x 3.5 x 10^5 Jkg^-1 Q = 3.5 x 10^5 J This means that the quantity of heat energy required to melt completely 1 kg of ice at -30°C is 3.5 x 10^5 J. However, we need to be careful in calculating the quantity of heat energy required to lower the temperature of the ice from 0°C to -30°C before it starts melting. To do this, we need to use the following formula: Q = m c ΔT Where Q is the quantity of heat energy, m is the mass of the substance, c is the specific heat capacity of ice, and ΔT is the change in temperature. We are given that the mass of the ice is 1 kg, the specific heat capacity of ice is 2.1 x 10^3 Jkg^-1K^-1, and the change in temperature is 30°C. So, substituting these values into the formula, we get: Q = 1 kg x 2.1 x 10^3 Jkg^-1K^-1 x 30 K Q = 6.3 x 10^4 J Therefore, the total quantity of heat energy required to melt completely 1 kg of ice at -30°C is the sum of the quantity of heat energy required to lower the temperature of the ice from 0°C to -30°C and the quantity of heat energy required to melt the ice. Total Q = 6.3 x 10^4 J + 3.5 x 10^5 J Total Q = 4.13 x 10^5 J So, the correct answer is 4.13 x 10^5 J.