A portable electric water heater transfers 255 watts (W) of power to 5.5 L of water, where 1 W = 1 J/s. How much time (in minutes) will it take for the water heater to heat the 5.5 L of water from 25 degrees celsius to 42 degrees celsius? (Assume that the water has a density of 1.0 g/mL)
How much heat is needed to raise the T of the water? That is
mass H2O(5500g) x specific heat H2O x (Tfinal-Tinitial) = q
255 J/s x #s = q
Solve for #seconds.
To find the time it takes for the water heater to heat the water, we need to use the equation:
Q = mcΔT
Where:
Q is the heat energy transferred to the water (in joules),
m is the mass of the water (in grams),
c is the specific heat capacity of water (in joules per gram per degree Celsius), and
ΔT is the change in temperature (in degrees Celsius).
First, we need to convert the volume of water from liters to grams, using the density of water. We know that 1 mL of water has a mass of 1 gram, so 5.5 L of water will have a mass of:
mass = volume × density
mass = 5.5 L × 1000 mL/L × 1 g/mL
mass = 5500 g
Next, we need to calculate the heat energy transferred to the water. We are given that the power of the water heater is 255 watts, which means that in 1 second, it transfers 255 joules of energy to the water. So, in t seconds:
Q = power × time
255 J = 255 W × t
t = 1 second
Now, we can calculate the change in temperature (ΔT). It is given that the initial temperature is 25 degrees Celsius and the final temperature is 42 degrees Celsius:
ΔT = final temperature - initial temperature
ΔT = 42°C - 25°C
ΔT = 17°C
Finally, we can substitute the values into the equation to find the time:
Q = mcΔT
255 J = 5500 g × c × 17°C
255 J = 93500 g°C × c
c = 255 J / (93500 g°C)
c ≈ 0.00273 J/g°C
Now, we can substitute the values of Q, m, c, and ΔT into the equation to solve for time (t):
Q = mcΔT
255 J = 5500 g × 0.00273 J/g°C × 17°C × t
255 J = 239.41 J × t
t ≈ 1.06 seconds
Therefore, it will take approximately 1.06 seconds for the water heater to heat the 5.5 L of water from 25 degrees Celsius to 42 degrees Celsius.