Your whole family has taken showers before you, dropping the temperature in the water heater to 18 degrees Celsius. If the water heater holds 150 kg of water, how much energy will it take to bring it to 50 degrees Celsius? If the energy is supplied by a 5 kW electric heating element, how long will it take?

Q = M*C*deltaT = 150 kg* 4184 J/kg*C*32 C

= ? J

Time = Q (J) /5000 J/s
The answer will be in seconds

099

To calculate the energy required to heat the water from 18 degrees Celsius to 50 degrees Celsius, you can use the formula:

Q = m * c * ΔT

where:
Q is the energy in Joules,
m is the mass of water in kilograms,
c is the specific heat capacity of water (4.186 J/g°C),
ΔT is the change in temperature in Celsius.

First, convert the mass of water from kilograms to grams:
150 kg * 1000 = 150,000 g

Then, calculate the energy:
Q = 150,000 g * 4.186 J/g°C * (50°C - 18°C)

Q = 150,000 g * 4.186 J/g°C * 32°C

Q = 199,392,000 J

Since 1 Joule (J) equals 1 Watt-second (Ws), you can convert the energy to kilowatt-hours (kWh) using the following conversion factor:

1 kWh = 3,600,000 J

Energy in kilowatt-hours:
199,392,000 J / 3,600,000 J/kWh = 55.39 kWh

To find out how long it will take to heat the water using a 5 kW electric heating element, you can use the formula:

t = E / P

where:
t is the time in hours,
E is the energy in kilowatt-hours,
P is the power in kilowatts.

Time in hours:
t = 55.39 kWh / 5 kW

t = 11.08 hours

Therefore, it will take approximately 11.08 hours to heat the water from 18 degrees Celsius to 50 degrees Celsius using a 5 kW electric heating element.

To calculate the amount of energy required to increase the temperature of water from 18 degrees Celsius to 50 degrees Celsius, we can use the formula:

Energy = mass × specific heat capacity × change in temperature

The specific heat capacity of water is approximately 4.186 J/g·°C.

First, we need to convert the mass of water from kg to grams:

Mass of water = 150 kg × 1000 g/kg = 150,000 g

Now, we can calculate the change in temperature:

Change in temperature = 50°C - 18°C = 32°C

Next, we can substitute the values into the formula to find the energy:

Energy = 150,000 g × 4.186 J/g·°C × 32°C
= 20,134,400 J

Since 1 watt-hour (Wh) is equal to 3600 joules (J), we can convert the energy from joules to kilowatt-hours (kWh):

Energy in kilowatt-hours (kWh) = 20,134,400 J / (3600 J/kWh)
≈ 5598 kWh

Now, let's calculate the time it would take to supply this energy using a 5 kW electric heating element.

Using the formula:

Time = Energy / Power

we can substitute the values:

Time = 5598 kWh / 5 kW
= 1119.6 hours

Therefore, it would take approximately 1119.6 hours to bring the water from 18 degrees Celsius to 50 degrees Celsius using a 5 kW electric heating element.