if 3.2 kcal of heat is added to 1kg of ice at 0 celcius, how much ice is produced and how much ice is left?
To determine how much ice is produced and how much ice is left when 3.2 kcal of heat is added to 1 kg of ice at 0 degrees Celsius, we need to consider the heat transfer and the phase changes involved.
The process of converting ice at 0 degrees Celsius into water at 0 degrees Celsius is known as melting. The specific heat capacity of ice is approximately 0.5 kcal/kg°C, which means it takes 0.5 kcal to raise the temperature of 1 kg of ice by 1 degree Celsius.
First, we need to calculate the amount of heat required to raise the temperature of the ice from -273 degrees Celsius (absolute zero) to 0 degrees Celsius. Since the specific heat capacity of ice is 0.5 kcal/kg°C, the heat required is:
Q1 = mass × specific heat capacity × temperature difference
= 1 kg × 0.5 kcal/kg°C × 0°C
= 0 kcal
Therefore, no heat is required to bring the ice from -273 degrees Celsius to 0 degrees Celsius. Moving forward, we can calculate the heat required for melting the ice at 0 degrees Celsius. The heat required for melting, also known as the latent heat of fusion, is 80 kcal/kg for water.
Q2 = mass × latent heat of fusion
= 1 kg × 80 kcal/kg
= 80 kcal
The total heat required for the ice to melt completely is 80 kcal. However, we have only added 3.2 kcal of heat. Therefore, we need to calculate the amount of ice that will melt with this addition of heat.
The proportion of ice that will melt can be calculated using the following equation:
Proportion of ice melted = (Heat added / Total heat required for melting)
Proportion of ice melted = (3.2 kcal / 80 kcal)
= 0.04
So, 0.04 kg of the ice will melt with the addition of 3.2 kcal of heat.
Now, we can determine the amount of ice produced and the amount of ice left:
Amount of ice produced = mass of ice melted
= 0.04 kg
Amount of ice left = initial mass of ice - mass of ice melted
= 1 kg - 0.04 kg
= 0.96 kg
Therefore, 0.04 kg of ice will melt, producing 0.04 kg of water, and 0.96 kg of ice will be left.