how much heat does it take to melt 4.2 kg of ice at 0c?

Answer in kcal

4.2 * heat of fusion of water

4.2 * 79.5 kcal/kg = 334 kCal

To find out how much heat it takes to melt 4.2 kg of ice at 0°C, we need to use the specific heat and the latent heat of fusion of ice.

1. First, let's determine the specific heat capacity of ice. The specific heat capacity (c) is the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius. For ice, the specific heat capacity is 2.09 J/g°C.

2. Next, we need to find the latent heat of fusion of ice. The latent heat of fusion (Lf) is the amount of heat required to convert 1 gram of a solid into a liquid at its melting point. For ice, the latent heat of fusion is 334 J/g.

3. Convert the given mass of ice from kilograms to grams. 1 kg is equal to 1000 grams, so 4.2 kg is equal to 4200 grams.

4. Calculate the heat required to raise the temperature of the ice from 0°C to its melting point using the formula: Q = m * c * ΔT.
- Q: heat energy
- m: mass (in grams)
- c: specific heat capacity (in J/g°C)
- ΔT: change in temperature
In this case, ΔT = (0°C - 0°C) = 0°C.
Therefore, Q = 4200 g * 2.09 J/g°C * 0°C = 0 J of heat.

5. Calculate the heat required to melt the ice using the formula: Q = m * Lf.
- Q: heat energy
- m: mass (in grams)
- Lf: latent heat of fusion (in J/g)
In this case, Q = 4200 g * 334 J/g = 1,406,800 J.

6. Convert the heat energy from joules to kilocalories (kcal). 1 kcal is equal to 4184 J.
Q = 1,406,800 J / 4184 J/kcal ≈ 336.33 kcal.

Therefore, it takes approximately 336.33 kcal of heat to melt 4.2 kg of ice at 0°C.