An electric heater warms a large 0 degree Celsius block of ice at the rate of 200J/s . calculate the mass of the ice that melts in 10 minutes
heat: 200J/s*10min*60se/min=200*600 J
heat: massice*Hf
solve for mass of ice after you set them equal.
Well, if an electric heater is warming a big ol' block of ice at a rate of 200J/s, we can first convert 10 minutes to seconds, which gives us 600 seconds.
Now, we know that the specific heat capacity of ice is about 2.09 J/g°C. To find the mass of ice that melts, we need to divide the total energy input by the heat capacity.
So, let's do some math: 200J/s * 600 seconds = 120,000 Joules.
Now, to find the mass, we divide the energy by the heat capacity: 120,000 J / 2.09 J/g°C = 57,416.27 grams.
So, approximately 57,416.27 grams (or about 57.42 kilograms) of ice would melt in 10 minutes. That's ice-melting action for you!
To calculate the mass of ice that melts, we need to determine the total energy required to melt the ice.
First, let's calculate the total energy required to raise the temperature of the ice from 0 degrees Celsius to the melting point of ice (0 degrees Celsius):
Given:
Rate of energy transfer (heating rate) = 200 J/s
Time = 10 minutes = 600 seconds
∆Q = P * t
∆Q = 200 J/s * 600 s
∆Q = 120,000 J
Next, let's calculate the energy required to melt the ice:
The specific heat capacity of ice is 2,090 J/(kg · °C) and the heat of fusion of ice is 334,000 J/kg.
The formula to calculate the energy required to melt the ice is:
Energy = mass * heat of fusion
Energy = 120,000 J
Heat of fusion = 334,000 J/kg
Thus, the mass of ice that melts can be calculated as:
mass = Energy / heat of fusion
mass = 120,000 J / 334,000 J/kg
mass ≈ 0.359 kg
Therefore, approximately 0.359 kg of ice will melt in 10 minutes.
To calculate the mass of the ice that melts, we can use the specific heat capacity of water and the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the heat energy is given as 200 J/s, and the temperature change is the difference between the initial temperature of 0 degrees Celsius and the melting point of ice, which is 0 degrees Celsius. Thus, ΔT = 0 - 0 = 0 degrees Celsius.
Since the ice is at its melting point, it needs additional heat energy to convert from solid ice to liquid water. The specific heat of fusion, denoted as Lf, is the amount of heat energy required to melt a unit mass of a substance at its melting point.
Knowing that the specific heat of fusion for ice is approximately 334,000 J/kg, we can use the formula Q = mLf to calculate the mass of ice that melts.
First, let's convert the time from minutes to seconds: 10 minutes × 60 seconds/minute = 600 seconds.
Using the equation Q = mcΔT, we find that the heat energy required to melt the ice is Q = (200 J/s) × (600 s) = 120,000 J.
Thus, we can calculate the mass of the ice that melts by rearranging the equation Q = mLf to m = Q / Lf:
m = (120,000 J) / (334,000 J/kg) = 0.359 kg.
Therefore, the mass of the ice that melts in 10 minutes is approximately 0.359 kg.