A 150L water heater is rated at 8kW. If 20%if its heat escapes, how long does the heater take to raise the temp of 150-L of water from 10 to 60 degrees C
48 degrees C
To calculate the time it takes for the water heater to raise the temperature of 150 liters of water from 10 to 60 degrees Celsius, you need to consider the amount of heat required.
The heat required to raise the temperature of a substance can be calculated using the formula:
Q = m * c * ΔT
Where:
Q = Heat required (in joules)
m = Mass of the substance (in kilograms)
c = Specific heat capacity of the substance (in J/kg·°C)
ΔT = Change in temperature (in °C)
First, convert the volume of water from liters to kilograms. Since the density of water is approximately 1 kg/L, the mass (m) of 150 liters of water is:
m = 150 kg
The specific heat capacity (c) of water is about 4.186 J/kg·°C.
The change in temperature (ΔT) is:
ΔT = 60°C - 10°C = 50°C
Next, calculate the heat required (Q):
Q = 150 kg * 4.186 J/kg·°C * 50°C
Now, we can calculate the time it takes for the heater to provide 8 kW of power or 8,000 joules per second.
Time = Q / (Power input of the heater * Efficiency)
The efficiency accounts for the heat loss. Since 20% of the heat escapes, the efficiency of the heater is:
Efficiency = 100% - 20% = 80% = 0.80 (decimal)
Now we can calculate the time:
Time = Q / (Power input of the heater * Efficiency)
Time = 150 kg * 4.186 J/kg·°C * 50°C / (8,000 J/s * 0.80)
Calculate the numerator:
150 kg * 4.186 J/kg·°C * 50°C = 313,950 J
Calculate the denominator:
8,000 J/s * 0.80 = 6,400 J/s
Now, substitute the values into the equation:
Time = 313,950 J / 6,400 J/s
Simplify the units:
Time = 49.05 s
Therefore, it would take approximately 49.05 seconds (or about 49 seconds) for the water heater to raise the temperature of 150 liters of water from 10 to 60 degrees Celsius.