What is the required resistance of an immersion heater that will melt 6.39 kg of ice at 0°C in 36 min while operating at 110 V?
im not too sure how to do this because delta_T=0. With the equations im using, i get 0 but its not the answer and im not quite sure what to do.
thanks for the help in advance.
Energy required to melt ice at zero degrees C = mass times heat of fusion of water.
To determine the required resistance of the immersion heater, we need to calculate the amount of heat required to melt the given mass of ice at 0°C.
The equation for calculating the heat required to melt a substance is given by:
Q = m * ΔHf
Where:
Q is the heat required (in joules),
m is the mass of the substance (in kilograms), and
ΔHf is the specific heat of fusion (or latent heat of fusion) of the substance (in joules per kilogram).
For ice, the specific heat of fusion (ΔHf) is approximately 334,000 J/kg.
So, the heat required to melt 6.39 kg of ice is:
Q = 6.39 kg * 334,000 J/kg
Now, since we are given a time of 36 minutes, we can calculate the power (P) required using the formula:
P = Q / t
Where:
P is the power required (in watts),
Q is the heat required (in joules), and
t is the time taken (in seconds).
Converting 36 minutes to seconds: 36 minutes * 60 seconds/minute = 2160 seconds.
Now we can calculate the power required:
P = (6.39 kg * 334,000 J/kg) / 2160 seconds
Finally, we can calculate the resistance (R) using Ohm's Law:
R = V^2 / P
Where:
R is the resistance (in ohms),
V is the voltage (in volts), and
P is the power required (in watts).
Plugging in the given values:
R = (110 V)^2 / P
By substituting the calculated value for P into the equation, you can find the required resistance of the immersion heater.
I hope this explanation helps!