How much energy must be put into a system to raise 100 g of solid water from 5.5 degrees Celsius to 75 Degrees Celsius?
Heat Capacity of Ice: 2.09 J/g degrees C
Heat Capacity of Water: 4.18 J/g degrees C
Heat of Fusion: 6.01 kJ/mol
To calculate the amount of energy required to raise the temperature of a substance, you need to consider the specific heat capacity of the substance and the change in temperature.
In this case, you are dealing with solid water (ice) and liquid water. Since the given mass is in grams, we can use the specific heat capacity in J/g degrees C.
1. First, calculate the energy required to heat the ice from 5.5 degrees Celsius to its melting point, 0 degrees Celsius.
Energy = mass × specific heat capacity × temperature change
Energy = 100 g × 2.09 J/g degrees C × (0 degrees C - 5.5 degrees C)
2. Next, you need to account for the energy required to change the state of the water from solid to liquid. This is known as the heat of fusion.
Energy = mass × heat of fusion
Energy = 100 g × 6.01 kJ/mol
Note that the given heat of fusion is in kJ/mol, so we need to convert grams to moles by using the molar mass of water (18.015 g/mol).
Moles = mass / molar mass
Moles = 100 g / 18.015 g/mol
Now multiply the moles by the heat of fusion:
Energy = moles × heat of fusion
3. Finally, calculate the energy required to heat the liquid water from its melting point to 75 degrees Celsius.
Energy = mass × specific heat capacity × temperature change
Energy = 100 g × 4.18 J/g degrees C × (75 degrees C - 0 degrees C)
Add up the energy from all three steps to get the total energy required to raise the temperature of 100 g of solid water from 5.5 degrees Celsius to 75 degrees Celsius.