2 kg of water at 5 celsius is added to ice at 0 celsius. The ice and water make up a closed system. Calculate how much of the ice melts
0.5
To calculate how much ice melts when 2 kg of water at 5 degrees Celsius is added to ice at 0 degrees Celsius, we need to consider the heat transfer that occurs between the water and ice.
The first step is to determine the amount of heat required to raise the temperature of the 2 kg of water from 5 degrees Celsius to 0 degrees Celsius. We can use the specific heat capacity of water to calculate this.
The specific heat capacity of water is approximately 4.18 Joules per gram per degree Celsius (J/g°C). Since we have 2000 grams of water (2 kg), we can calculate the heat transferred using the equation:
Q1 = mass × specific heat capacity × change in temperature
Q1 = 2000 g × 4.18 J/g°C × (0°C - 5°C)
Q1 = -41,800 Joules
The negative sign indicates that heat is lost from the water.
Next, we need to consider the heat transfer that occurs when the ice melts. The heat required to melt a substance is given by its heat of fusion. For ice, the heat of fusion is approximately 334 J/g. Since we are considering the mass of the ice that melts, we can calculate the heat transferred using the equation:
Q2 = mass × heat of fusion
We don't know the mass of the ice that melts, so let's assume it is 'm' grams. Therefore, we have:
Q2 = m g × 334 J/g
Q2 = 334 m Joules
In a closed system, the total amount of heat lost by the water (Q1) is equal to the total amount of heat gained by the ice (Q2). Therefore, we can equate the two equations:
Q1 = Q2
-41,800 Joules = 334 m Joules
Solving for 'm', we get:
m = -41,800 Joules / 334 J/g
m ≈ -125 g
The negative sign indicates that the ice melts, so we take the absolute value of 'm':
m ≈ 125 g
Therefore, approximately 125 grams of ice will melt when 2 kg of water at 5 degrees Celsius is added to ice at 0 degrees Celsius in a closed system.
the sum of heats gained is zero (remember one of those has heat lost).
Heat gained by ice+heat gained by water=0
Hv*massicemelted+masswater*Cwater*(0-5)=0
solve for massicemelted.