Show that 9300 cal is required to change 15g of 20C water to 100C steam
To show that 9300 calories are required to change 15 grams of water at 20°C to steam at 100°C, we need to calculate the amount of heat energy required at each stage of the process using the specific heat capacity and heat of vaporization of water.
First, let's calculate the heat energy required to raise the temperature of 15 grams of water from 20°C to 100°C.
The specific heat capacity of water is 1 calorie/gram°C. Therefore, the heat energy required to raise the temperature of 15 grams of water by ΔT degrees is given by:
Q1 = mass * specific heat capacity * ΔT
= 15 g * 1 cal/g°C * (100°C - 20°C)
= 15 g * 1 cal/g°C * 80°C
= 1200 cal
So, it takes 1200 calories to raise the temperature of 15 grams of water from 20°C to 100°C.
Next, we need to calculate the heat energy required to convert 15 grams of water at 100°C to steam at 100°C. The heat of vaporization of water is 540 calories/gram.
Q2 = mass * heat of vaporization
= 15 g * 540 cal/g
= 8100 cal
So, it takes 8100 calories to convert 15 grams of water at 100°C to steam at 100°C.
Adding the heat energy required for both processes:
Total heat energy = Q1 + Q2
= 1200 cal + 8100 cal
= 9300 cal
Therefore, it takes 9300 calories to change 15 grams of water at 20°C to steam at 100°C.