Suppose you put a 100 W light bulb in a container of water and use it to heat the water. How long would it take to raise the temperature of a gallon of water at 25 C to 90C?
Please explain!
To calculate the time it would take to raise the temperature of a gallon of water from 25°C to 90°C using a 100 W light bulb, you need to consider the amount of energy required and the power output of the bulb.
First, calculate the amount of energy needed to raise the temperature of the water. This can be done using the equation:
Q = mcΔT
Where:
Q is the heat energy required
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
For simplicity, let's assume that the mass of a gallon of water is approximately 3.785 kg and the specific heat capacity of water is 4.18 J/g°C.
Q = (3.785 kg) * (4.18 J/g°C) * (90°C - 25°C)
Q = 3932.37 kJ
Since 1 watt-hour (Wh) is equal to 3.6 kJ, let's convert the energy required to watt-hours:
Q = 3932.37 kJ / 3.6 kJ/Wh
Q = 1092.33 Wh
Next, we need to calculate the time using the power output of the light bulb:
P = W/t
Where:
P is the power output of the light bulb (100 W)
W is the work done (energy required)
t is the time taken
Rearranging the equation, we can calculate t:
t = W / P
t = 1092.33 Wh / 100 W
t = 10.92 hours
Therefore, it would take approximately 10.92 hours to raise the temperature of a gallon of water from 25°C to 90°C using a 100 W light bulb.