How many kilojoules of heat energy are needed to change 49.6 g of ice at 15 degrees celsius to water at 58 degrees celsius?
I am having trouble figuring out how to solve this.
I can't help because I'm confused by the problem. How can you have ice at 15 C? You can't. You must have made a typo; I suspect it is -15 C.
Here is the general procedure.
For change of state (change of phase), heat needed is
q = mass x heat fusion (if melting/freezing) or heat of vaporization (if vaporizing/condensing) and if moving within a phase (the same state)
q = mass x specific heat x (Tfinal-Tinitial).
Then total Q = sum of individual qs.
To calculate the amount of heat energy required to change the state and temperature of a substance, we can use the equation:
Q = mcΔT
Where Q represents the heat energy, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, we need to consider two separate processes: melting the ice (changing state) and then heating the liquid water.
First, let's calculate the heat energy required to change the state of ice to water:
1. Determine the heat energy needed for the phase change (melting):
Q1 = m × ΔHfus
Where m is the mass of the ice and ΔHfus is the heat of fusion (the energy required to change 1 gram of ice at 0 degrees Celsius to water at 0 degrees Celsius). The heat of fusion for ice is approximately 334 J/g.
Q1 = (mass of ice) × 334 J/g
2. Calculate the heat energy required to raise the temperature of the water from 0 degrees Celsius to the final desired temperature (58 degrees Celsius):
Q2 = m × c × ΔT
Where c is the specific heat capacity of water and ΔT is the change in temperature.
The specific heat capacity of water is approximately 4.18 J/(g·°C).
Q2 = (mass of water) × 4.18 J/(g·°C) × (58 - 0) °C
3. Add the two calculated heat energies together to get the total:
Total heat energy = Q1 + Q2
Now, let's plug in the given values:
Mass of ice = 49.6 g
Initial temperature (T1) = 15°C
Final temperature (T2) = 58°C
Calculating Q1:
Q1 = 49.6 g × 334 J/g
Calculating Q2:
ΔT = (58°C - 0°C) = 58°C
Q2 = 49.6 g × 4.18 J/(g·°C) × 58°C
Finally, add Q1 and Q2 to find the total heat energy required to change the ice to water and heat it up to the final temperature.