How much heat is required to convert solid ice with a mass of 875 g and at a temperature of -11.5 °C to liquid water at a temperature of 52.0 °C? (The specific heat of ice is cice = 2100 J/kgK, the specific heat of water is cwater = 4186.8 J/kgK, and the heat of fusion for water is: Lf = 334 kJ/kg.)
I did -> (.875)(2100)(325-261.5) = 116681J
then (.875)(334000)= 292250J
then added those two answers together and got 408931J and it keeps saying that is wrong..
It is wrong.
figure
a. heat to heat ice to 0C from -11.5
Note: there is no reason to conver to K. One kelvin change is exactly one C change.
Then heat to melt the ice at 0C
then to heat the water from 0 C to 52 C
add them up.
To calculate the heat required to convert solid ice to liquid water, we need to consider two steps:
Step 1: Raise the temperature of the ice from -11.5 °C to 0 °C.
Step 2: Convert the ice at 0 °C to water at 52.0 °C.
Let's calculate:
Step 1:
The heat required to raise the temperature of the ice from -11.5 °C to 0 °C can be calculated using the formula: Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Using the given values:
Q1 = (mass of ice)(specific heat of ice)(change in temperature)
= (0.875 kg)(2100 J/kg°C)(0 - (-11.5) °C)
= (0.875 kg)(2100 J/kg°C)(11.5 °C)
≈ 26737.5 J
Step 2:
The heat required to convert the ice at 0 °C to water at 52.0 °C can be calculated using the formula: Q = mL, where Q is the heat, m is the mass, and L is the heat of fusion.
Using the given values:
Q2 = (mass of ice)(heat of fusion)
= (0.875 kg)(334 kJ/kg)
= (0.875 kg)(334000 J/kg)
= 292250 J
To find the total heat required, we add the heat from Step 1 and Step 2:
Total heat = Q1 + Q2
= 26737.5 J + 292250 J
≈ 318987.5 J
Therefore, the correct answer is approximately 318987.5 J, not 408931 J.
To find the total heat required to convert solid ice at -11.5 °C to liquid water at 52.0 °C, you need to consider three steps:
1. Heating the ice from -11.5 °C to 0 °C:
Heat = mass * specific heat of ice * temperature difference
Heat = 0.875 kg * 2100 J/kgK * (0 °C - (-11.5 °C))
Heat = 0.875 kg * 2100 J/kgK * 11.5 °C
Heat = 20,137.5 J
2. Melting the ice at 0 °C to liquid water at 0 °C:
Heat = mass * heat of fusion for water
Note: The heat of fusion is given in kJ/kg, so we need to convert it to J/kg.
Heat = 0.875 kg * (334,000 J/kg / 1,000)
Heat = 292,250 J
3. Heating the water from 0 °C to 52.0 °C:
Heat = mass * specific heat of water * temperature difference
Heat = 0.875 kg * 4186.8 J/kgK * (52.0 °C - 0 °C)
Heat = 0.875 kg * 4186.8 J/kgK * 52.0 °C
Heat = 192,033.6 J
Now, add all the heats together to obtain the total heat required:
Total Heat = 20,137.5 J + 292,250 J + 192,033.6 J
Total Heat = 504,421.1 J
Therefore, the correct answer is 504,421.1 J.