How Much Heat is Required to Convert Ice at 0°C to 30°C Water?
Converting ice at 0°C to water at 30°C involves two key steps: first, melting the ice, and second, heating the water to the desired temperature. This process requires a specific amount of heat, which can be calculated using basic thermodynamics. Let's explore the calculation in detail and address related concepts.
Step 1: Melting the Ice
Melting ice to water at 0°C involves the latent heat of fusion. The latent heat of fusion for ice is approximately 334 J/g. This means 334 joules of energy are required to convert each gram of ice to water at 0°C without changing its temperature.
The formula used for this calculation is: Q1 m · Lf
Q1: Heat required to melt the ice (Joules) m: Mass of ice (grams) Lf: Latent heat of fusion of ice (Joules/gram)Given the mass of ice is 15 grams:
Q1 15 g · 334 J/g 5010 J
Step 2: Heating the Water
After the ice has been melted, the next step is to heat the water from 0°C to 30°C. The specific heat capacity of water is approximately 4.18 J/g°C. This means that 4.18 joules of energy are required to raise the temperature of 1 gram of water by 1°C.
The formula used for this calculation is: Q2 m · c · ΔT
Q2: Heat required to raise the temperature (Joules) m: Mass of water (grams) c: Specific heat capacity of water (Joules/gram°C) ΔT: Change in temperature (°C)Given the mass of water is 15 grams and the change in temperature is 30°C:
Q2 15 g · 4.18 J/g°C · 30°C 1881 J
Total Heat Required
To find the total heat required, we sum the heat required for both steps:
Q Q1 Q2 5010 J 1881 J 6891 J
Conclusion: The total heat required to convert 15 grams of ice at 0°C to water at 30°C is approximately 6891 joules.
Further Concepts: Latent Heat of Fusion and Specific Heat Capacity
Latent Heat of Fusion: Latent heat of fusion is the amount of energy required to change a substance from the solid to the liquid state without changing its temperature. For ice, this value is approximately 334 J/g.
Specific Heat Capacity: Specific heat capacity is the amount of energy required to raise the temperature of a substance by 1°C. For water, this value is approximately 4.18 J/g°C.
Understanding these concepts and applying them correctly is crucial for accurately calculating the heat required in various scenarios involving phase changes and temperature changes.