A small electric immersion heater is used to boil 191.0 g of water for a cup of instant coffee. The heater is labeled 355.0 W, which means that it converts electrical energy to heat at this rate. Calculate the time required to bring this water from 12.0°C to the boiling point ignoring any heat losses.
heaterpower*time=masswater*c*(tfinal-12)
solve for time (in seconds)
To calculate the time required to bring the water from 12.0°C to the boiling point using the given electric immersion heater, you can use the formula:
Q = m * c * ΔT
where:
Q = heat energy (in joules)
m = mass of water (in grams)
c = specific heat capacity of water (4.184 J/g°C)
ΔT = change in temperature (in °C)
First, let's calculate the heat energy required to raise the temperature of the water from 12.0°C to the boiling point. The boiling point of water is 100°C, so the change in temperature (ΔT) is:
ΔT = 100°C - 12.0°C = 88.0°C
Next, plug the values into the formula:
Q = 191.0 g * 4.184 J/g°C * 88.0°C
Q = 67107.632 J
Now, we need to calculate the time required using the power (P) of the electric immersion heater:
P = Q / t
Rearranging the formula, we get:
t = Q / P
Substituting the values:
t = 67107.632 J / 355.0 W
t ≈ 188.987 seconds
Therefore, it would take approximately 189 seconds (rounded to the nearest whole number) to bring the water from 12.0°C to the boiling point using the given electric immersion heater.