what is the heat required in kilo calories to covert 2kg of ice at 0 c completely into stream at 100c
To calculate the heat required to convert a substance from one state to another, we need to consider the specific heat capacity of each state and the phase change. Here are the steps to calculate the heat required to convert 2kg of ice at 0°C into steam at 100°C:
1. Heating the ice from 0°C to 0°C (melting point):
The specific heat capacity of ice is 2.09 calories/gram·°C. Since we have 2kg of ice (2,000 grams), the heat required can be calculated using the formula:
Heat = mass × specific heat capacity × change in temperature.
The change in temperature is (0°C - 0°C) = 0.
Therefore, the heat required to heat the ice from 0°C to 0°C is:
Heat = 2,000 grams × 2.09 calories/gram·°C × 0°C = 0 calories.
2. Melting the ice at 0°C:
The heat required to melt the ice at its melting point is given by the formula:
Heat = mass × heat of fusion.
The heat of fusion of ice is 79.7 calories/gram.
Thus, the heat required to convert 2kg of ice at 0°C into water at 0°C is:
Heat = 2,000 grams × 79.7 calories/gram = 159,400 calories.
3. Heating the water from 0°C to 100°C:
The specific heat capacity of water is 1 calorie/gram·°C. The change in temperature is (100°C - 0°C) = 100°C.
So, the heat required to heat 2kg of water from 0°C to 100°C is:
Heat = 2,000 grams × 1 calorie/gram·°C × 100°C = 200,000 calories.
4. Vaporizing the water at 100°C:
The heat required to vaporize water at its boiling point is given by the formula:
Heat = mass × heat of vaporization.
The heat of vaporization of water is 540 calories/gram.
Hence, the heat required to convert 2kg of water at 100°C into steam at 100°C is:
Heat = 2,000 grams × 540 calories/gram = 1,080,000 calories.
To find the total heat required, you need to add up the heats calculated from each step:
Total heat = Heat in step 1 + Heat in step 2 + Heat in step 3 + Heat in step 4
Total heat = 0 calories + 159,400 calories + 200,000 calories + 1,080,000 calories
Total heat = 1,439,400 calories.
Therefore, the heat required to convert 2kg of ice at 0°C completely into steam at 100°C is 1,439,400 calories.