How many kilo calories (kcal) are required to change 1 kg of 0°C ice to 0°C water?
heat of fusion for ice is ... 333.5 kJ/kg
1 kJ = 239 cal
To calculate the number of kilocalories (kcal) required to change 1 kg of 0°C ice to 0°C water, we need to consider the specific heat capacity and the heat of fusion of ice.
The specific heat capacity (c) of ice is approximately 2.09 Joule/(gram·°C) or 0.5 kcal/(kg·°C). The heat of fusion (ΔHf) of ice is 333.5 Joules/gram or 79.7 kcal/kg.
First, we need to calculate the amount of energy required to raise the temperature of 1 kg of ice from 0°C to its melting point, 0°C:
Energy (Q1) = mass (m) × specific heat capacity (c) × temperature change (ΔT)
= 1000 g × 0.5 kcal/(kg·°C) × (0°C - 0°C)
= 0 kcal
Next, we need to calculate the amount of energy required for the phase change from solid ice to liquid water:
Energy (Q2) = mass (m) × heat of fusion (ΔHf)
= 1000 g × 79.7 kcal/kg
= 79.7 kcal
Therefore, the total kilocalories required to change 1 kg of 0°C ice to 0°C water is 0 kcal + 79.7 kcal = 79.7 kcal.
To find the number of kilocalories (kcal) required to change 1 kg of 0°C ice to 0°C water, we can use the concept of specific heat and latent heat.
The specific heat capacity of ice is approximately 2.09 kcal/kg°C, meaning it takes 2.09 kcal to raise the temperature of 1 kg of ice by 1°C. However, in this case, we are not changing the temperature of the ice, but rather undergoing a phase change from solid (ice) to liquid (water).
The specific latent heat of fusion for ice is approximately 333.5 kcal/kg, which means it takes 333.5 kcal to change 1 kg of ice at 0°C to 1 kg of water at 0°C without changing the temperature.
Therefore, to calculate the total kilocalories required, we need to add the amount of energy required to raise the temperature of the ice from 0°C to its melting point (0°C) to the energy required to undergo the phase change.
Total energy required = (Energy required to raise temperature) + (Energy required for phase change)
Energy required to raise temperature = Mass × Specific heat capacity × Temperature change
= 1 kg × 2.09 kcal/kg°C × (0°C - 0°C) = 0 kcal
Energy required for phase change = Mass × Specific latent heat
= 1 kg × 333.5 kcal/kg = 333.5 kcal
Total energy required = 0 kcal + 333.5 kcal = 333.5 kcal
Hence, it takes 333.5 kilocalories (kcal) to change 1 kg of 0°C ice to 0°C water.