the heating element of a coffee maker operates at 120 V and carries a current of 2 A. Assuming that the water absorbs all of the energy converted by the resistor, calculate how long it takes to heat .500 kg of water from room temperature 23 degrees C to the boiling point.
heat= power*time=120*2*time
but heat also = .500kg(cwater)(77)
set the equal, solve for time.
To calculate the time it takes to heat the water, we first need to find the amount of energy required. The formula to calculate the energy is given by:
Energy = Mass x Specific Heat x Change in Temperature
Where:
- Mass is the mass of water (0.500 kg),
- Specific Heat is the specific heat capacity of water (4.18 J/g °C),
- Change in Temperature is the final temperature minus the initial temperature.
In this case, the final temperature will be the boiling point of water, which is 100 °C, and the initial temperature is 23 °C.
First, let's convert the mass to grams:
Mass = 0.500 kg x 1000 g/kg = 500 g
Now, let's calculate the change in temperature:
Change in Temperature = Final Temperature - Initial Temperature
Change in Temperature = 100 °C - 23 °C = 77 °C
Now, we can calculate the energy:
Energy = Mass x Specific Heat x Change in Temperature
Energy = 500 g x 4.18 J/g °C x 77 °C
Next, we need to convert the energy into units of work done by the heating element. Since power is given by the formula:
Power = Voltage x Current
we can rearrange the formula to solve for time:
Time = Energy / Power
The power is given by the formula:
Power = Voltage x Current = 120 V x 2 A = 240 W
Now we can calculate the time:
Time = Energy / Power
Time = (500 g x 4.18 J/g °C x 77 °C) / 240 W
After performing the calculations, we can determine the time it takes to heat the water.