To calculate the heat required to raise the temperature of ice to water, we need to consider two processes: (1) heating the ice to its melting point, and (2) melting the ice into water. Each process requires a specific amount of heat.
- Heating the ice to its melting point: The specific heat capacity of ice is approximately 2.09 J/g°C. Since the initial temperature is 0°C, we need to calculate the heat required to raise the temperature of the ice to its melting point, which is 0°C.
Heat = mass × specific heat capacity × temperature change Heat = 5 g × 2.09 J/g°C × (0°C - 0°C) Heat = 0 J
No heat is required to raise the ice's temperature to its melting point since it is already at 0°C.
- Melting the ice into water: To melt the ice, we need to calculate the heat required for the phase change. The heat of fusion, also known as the latent heat of fusion, for ice is approximately 334 J/g.
Heat = mass × heat of fusion Heat = 5 g × 334 J/g Heat = 1670 J
So, 1670 joules of heat are required to melt 5 grams of ice at 0°C into water at 0°C.
Now, to heat the water from 0°C to 10°C: The specific heat capacity of water is approximately 4.18 J/g°C. We'll use this value to calculate the heat required to raise the temperature of the water.
Heat = mass × specific heat capacity × temperature change Heat = 5 g × 4.18 J/g°C × (10°C - 0°C) Heat = 209 J
Therefore, an additional 209 joules of heat are required to raise the temperature of 5 grams of water from 0°C to 10°C.
To find the total heat required, we add the heat required for melting and the heat required for heating the water:
Total heat = Heat for melting + Heat for heating Total heat = 1670 J + 209 J Total heat = 1879 J
Therefore, a total of 1879 joules of heat are needed to take 5 grams of ice at 0°C to water at 10°C.