Show that 9300 cal is required to change 15 g of 20° C water to 100° C steam.
To show that 9300 calories (cal) is required to change 15 grams (g) of 20°C water to 100°C steam, we can calculate the amount of heat energy needed for each phase transition:
1. Heating the water from 20°C to its boiling point:
The specific heat capacity of water is approximately 1 calorie per gram per degree Celsius (cal/g°C). Therefore, to heat 15 grams of water from 20°C to its boiling point (100°C), we can use the formula:
Heat energy = mass × specific heat capacity × temperature change
Heat energy = 15 g × 1 cal/g°C × (100°C - 20°C)
Heat energy = 15 g × 1 cal/g°C × 80°C
Heat energy = 1200 cal
So, to heat the water to its boiling point, we need 1200 calories.
2. Changing the water at its boiling point to steam:
The heat of vaporization of water is approximately 540 calories per gram (cal/g). Thus, to convert 15 grams of water at its boiling point (100°C) to steam, we can use the formula:
Heat energy = mass × heat of vaporization
Heat energy = 15 g × 540 cal/g
Heat energy = 8100 cal
Therefore, to change the water to steam, we need 8100 calories.
To get the total energy required to change 15 grams of 20°C water to 100°C steam, we add the heat energy required for each phase transition:
Total heat energy = Heat energy for heating water + Heat energy for changing to steam
Total heat energy = 1200 cal + 8100 cal
Total heat energy = 9300 cal
Hence, the total energy required is indeed 9300 calories to change 15 grams of 20°C water to 100°C steam.