Assume that you take a 10.0g ice cube out of the freezer at -10 C. How much ice would be left unmelted after you added 340 J of energy?
First the ice cube must be heated from -10 C to zero C.
q = mass x specific heat x delta T.
This will give you the heat required to do just that. Subtract q required from 340 J to obtain the heat remaining to melt the ice cube.
Then q = mass x heat of fusion for ice.
Plug in q from above, calculate mass ice melted, subtract from 10 to determine how much ice remains unmelted at zero.
Post your work if you get stuck.
To determine how much ice would be left unmelted after adding 340 J of energy, we need to consider the energy required to melt the ice.
First, we need to calculate the amount of energy needed to raise the temperature of the ice cube from its initial temperature of -10°C to its melting point, which is 0°C. The specific heat capacity of ice is 2.09 J/g°C.
The formula to calculate this energy is:
Energy = mass × specific heat capacity × temperature change
The mass of the ice cube is given as 10.0 g, the specific heat capacity of ice is 2.09 J/g°C, and the temperature change is 0°C - (-10°C) = 10°C.
So the energy required to raise the temperature of the ice cube to its melting point is:
Energy = 10.0 g × 2.09 J/g°C × 10°C = 209 J
Next, we need to calculate the energy required to melt the ice cube. The heat of fusion for water is 334 J/g.
The formula to calculate this energy is:
Energy = mass × heat of fusion
The mass of the ice cube is 10.0 g, and the heat of fusion for water is 334 J/g.
So the energy required to melt the ice cube is:
Energy = 10.0 g × 334 J/g = 3340 J
To find out how much ice would be left unmelted, we subtract the total energy required to raise the temperature and melt the ice cube from the energy added (340 J).
Energy added = 340 J
Total energy required = energy to raise temperature + energy to melt ice
Total energy required = 209 J + 3340 J = 3549 J
Finally, we subtract the total energy required from the energy added:
Unmelted ice = Energy added - Total energy required
Unmelted ice = 340 J - 3549 J = -3209 J
Since the value is negative, it means that the energy added is insufficient to raise the temperature of the ice cube to its melting point and melt the ice. Therefore, all the ice would remain unmelted in this scenario.