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 = ...
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 = 2.1x10 3Jkg -1K -1]
Answer Details
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.