An electric heater used to boil small amounts of water consists of a 25-Ω coil that is immersed directly in the water. It operates from a 60-V socket. How much time is required for this heater to raise the temperature of 0.50 kg of water from 29° C to the normal boiling point?
i = V/R = 60/25 = 2.4 amps
P = i v = 2.4*60 = 144 watts or Joules/second
Joules into water = 144 t
where t is in seconds
144 t = C (.5)(100-29)
I do not recall C, specific heat of water
in Joules/ kilogram deg centigrade
t(seconds) = ((kg water)(temp change)(4186))/Watts
Watts = V^2/ohms
To calculate the time required for the heater to raise the temperature of the water, we can use the formula:
Q = mcΔT
where:
Q is the heat energy required,
m is the mass of the water (0.50 kg),
c is the specific heat capacity of water (4186 J/kg°C),
and ΔT is the change in temperature (the difference between the final and initial temperatures).
To find the heat energy required, we can use the formula:
Q = IVt
where:
I is the current flowing through the heater coil,
V is the voltage across the coil,
and t is the time.
First, we need to calculate the current flowing through the coil:
I = V/R
where:
R is the resistance of the coil (25 Ω).
I = 60 V / 25 Ω = 2.4 A
Next, we can calculate the heat energy required:
Q = IVt
Since the resistance R is equal to the voltage V divided by the current I, we have:
R = V / I = 60 V / 2.4 A = 25 Ω
Therefore, the heat energy required is:
Q = IVt = (2.4 A)(60 V)t = 144t J
We know that Q = mcΔT, so we can set up the equation:
mcΔT = 144t
Substituting the given values:
(0.50 kg)(4186 J/kg°C)(100°C - 29°C) = 144t
(0.50 kg)(4186 J/kg°C)(71°C) = 144t
149,253 J = 144t
Finally, we can solve for t:
t = 149,253 J / 144 = 1037.34 seconds
Therefore, it will take approximately 1037.34 seconds (or about 17 minutes and 17 seconds) for the heater to raise the temperature of the water from 29°C to the normal boiling point.
To find out how much time is required for the heater to raise the temperature of the water, we need to calculate the amount of heat required and then use the power of the heater to determine the time.
Step 1: Calculate the amount of heat required.
The amount of heat required can be calculated using the formula:
Q = mcΔT
Where:
Q = amount of heat (in Joules)
m = mass of water (in kg)
c = specific heat capacity of water (equal to 4186 J/kg°C)
ΔT = change in temperature (in °C)
Given:
m = 0.50 kg
ΔT = boiling point of water (100°C) - initial temperature (29°C) = 71°C
So, Q = (0.50 kg)(4186 J/kg°C)(71°C) = 148,465 J
Step 2: Calculate the power of the heater.
The power of the heater can be calculated using the formula:
P = V^2/R
Where:
P = power (in Watts)
V = voltage (in volts)
R = resistance (in ohms)
Given:
V = 60 V
R = 25 Ω
So, P = (60 V)^2 / 25 Ω = 144 W
Step 3: Calculate the time required.
To find the time required to generate the required amount of heat, we can use the formula:
t = Q / P
Where:
t = time (in seconds)
Q = amount of heat (in Joules)
P = power (in Watts)
Using the values from step 1 and step 2:
t = 148,465 J / 144 W = 1029.9 seconds
Therefore, it would take approximately 1030 seconds, or approximately 17 minutes and 10 seconds, for the heater to raise the temperature of 0.50 kg of water from 29°C to the normal boiling point.