What amount of heat is required to melt 100 g of ice at 0°C into water at 25°C? The specific heat of ice is approximately 2.09 J/g°C.
To calculate the amount of heat required to melt 100 g of ice at 0°C into water at 25°C, we need to consider both the heat required for the phase change (melting the ice) and the heat required to raise the temperature of the resulting water.
First, let's calculate the heat required for the phase change, known as the heat of fusion. The heat of fusion for ice is 334 J/g. This means that 334 Joules of energy are required to convert 1 gram of ice at 0°C into water at 0°C.
To find the heat required to melt 100 g of ice, we can use the formula:
Heat for phase change = mass × heat of fusion
Heat for phase change = 100 g × 334 J/g
Heat for phase change = 33,400 J
So, 33,400 Joules of energy are required to melt the 100 g of ice at 0°C into water at 0°C.
Next, let's calculate the heat required to raise the temperature of the resulting water from 0°C to 25°C. The specific heat capacity of water is approximately 4.18 J/g°C. This means that 4.18 Joules of energy are required to raise the temperature of 1 gram of water by 1°C.
To find the heat required to raise the temperature of the water, we can use the formula:
Heat for temperature change = mass × specific heat capacity × temperature change
Heat for temperature change = 100 g × 4.18 J/g°C × (25°C - 0°C)
Heat for temperature change = 10,450 J
Therefore, 10,450 Joules of energy are required to raise the temperature of the resulting water from 0°C to 25°C.
Finally, to get the total heat required, we can add the heat required for the phase change and the heat required for the temperature change:
Total heat required = Heat for phase change + Heat for temperature change
Total heat required = 33,400 J + 10,450 J
Total heat required = 43,850 J
Therefore, approximately 43,850 Joules of heat energy are required to melt 100 g of ice at 0°C into water at 25°C.
To calculate the amount of heat required to melt the ice and raise the water temperature, we need to consider two steps: (1) the heat required to melt the ice and (2) the heat required to raise the temperature of the water.
1. Heat required to melt the ice:
The heat required to melt the ice can be calculated using the formula:
Q = m * ΔH_fus
where:
Q is the amount of heat required (in Joules),
m is the mass of the ice (in grams),
ΔH_fus is the heat of fusion (amount of heat required to melt one gram of ice at 0°C).
Given:
m = 100 g
ΔH_fus = 334 J/g (the heat of fusion for ice)
Plugging in the values:
Q = 100 g * 334 J/g
Q = 33,400 J
Therefore, the amount of heat required to melt 100 g of ice is 33,400 Joules.
2. Heat required to raise the temperature of water:
The heat required to raise the temperature of the water can be calculated using the formula:
Q = m * c * ΔT
where:
Q is the amount of heat required (in Joules),
m is the mass of water (in grams),
c is the specific heat of water (approximately 4.18 J/g°C),
ΔT is the change in temperature (25°C - 0°C = 25°C).
Given:
m = 100 g
c = 4.18 J/g°C
ΔT = 25°C
Plugging in the values:
Q = 100 g * 4.18 J/g°C * 25°C
Q = 10,450 J
Therefore, the amount of heat required to raise the temperature of 100 g of water from 0°C to 25°C is 10,450 Joules.
Adding both steps together:
Total amount of heat required = heat to melt the ice + heat to raise the temperature of water
Total amount of heat required = 33,400 J + 10,450 J
Total amount of heat required = 43,850 J
Therefore, the total amount of heat required to melt 100 g of ice at 0°C into water at 25°C is 43,850 Joules.