To calculate the amount of heat required to turn one liter of cold water into one liter of steam, we need to consider the specific heat capacity of water and the heat of vaporization.
- Heating the Water: The specific heat capacity of water is approximately 4.18 joules/gram·°C. Since we are dealing with one liter of water, which is equivalent to 1000 grams, we can use the same specific heat capacity. Therefore, the heat required to raise the temperature of one liter of water from its initial temperature (let's assume it's 25°C) to its boiling point (100°C) can be calculated using the formula:
Q1 = mass × specific heat capacity × temperature change
Q1 = 1000 g × 4.18 J/g·°C × (100°C - 25°C)
Q1 = 313,500 joules
- Vaporizing the Water: The heat of vaporization of water is approximately 2260 joules/gram. Since we have one liter of water (1000 grams), the heat required to vaporize the water at its boiling point is:
Q2 = mass × heat of vaporization
Q2 = 1000 g × 2260 J/g
Q2 = 2,260,000 joules
- Total Heat Required: To calculate the total heat required to turn one liter of cold water into one liter of steam, we add Q1 and Q2:
Total Heat = Q1 + Q2
Total Heat = 313,500 joules + 2,260,000 joules
Total Heat = 2,573,500 joules
Therefore, approximately 2,573,500 joules of heat are required to turn one liter of cold water (at 25°C) into one liter of steam at its boiling point (100°C).