What is the cost of electrical heating 50 liters of water from 40degree celsius to 100degree celsius at USD 8.0 /kwh?
Cost = (energy added in kw-hours)/(cost per kwatt-hour)
The number of kwatt-hours is
Q = 50,000 g * 60 C * 4.184 J/cal * 1.00 cal/g*C *10^-3 kj/j*1/3600 h/s)
= 3.49 kw-h
You might not have copied the cost per kw-h correctly. It is more likely to be 8 cents than 8 dollars.
This looks like roughly the cost of filling a bath tub with hot water.
thank you very much my friend.
To calculate the cost of heating 50 liters of water from 40 degrees Celsius to 100 degrees Celsius, we need to consider the heat energy required and the cost of electricity.
1. Calculate the heat energy required:
The heat energy required to heat a substance can be calculated using the formula:
Energy (Q) = mass (m) x specific heat capacity (c) x change in temperature (ΔT)
In this case, the mass of water is 50 liters, which can be converted to kilograms:
1 liter = 1 kilogram (density of water)
50 liters = 50 kilograms
The specific heat capacity of water is approximately 4.186 joules per gram-degree Celsius.
Converting the mass to grams:
50 kilograms = 50,000 grams
The change in temperature is the difference between the final and initial temperatures:
ΔT = 100 degrees Celsius - 40 degrees Celsius = 60 degrees Celsius
Using the formula, we can calculate the heat energy required:
Q = 50,000 grams x 4.186 J/g°C x 60°C = 12,558,000 joules (or 12.56 megajoules)
2. Convert the energy to kilowatt-hours (kWh):
1 kilowatt-hour (kWh) = 3,600,000 joules
So, 12.56 megajoules = 12,560,000 joules = 12,560,000 joules / 3,600,000 joules = 3.49 kWh
3. Calculate the cost of electricity:
Given that the cost is USD 8.0 per kWh, we can multiply the energy required by the cost per kWh to find the total cost:
3.49 kWh x USD 8.0/kWh = USD 27.92
Therefore, the cost of heating 50 liters of water from 40 degrees Celsius to 100 degrees Celsius at USD 8.0/kWh is approximately USD 27.92.
To calculate the cost of electrical heating for 50 liters of water, we need to consider the energy required to raise the temperature from 40 degrees Celsius to 100 degrees Celsius and then convert it into the cost in USD.
First, we need to calculate the energy required using 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 (approximately 4.18 J/g·°C or 4180 J/kg·°C)
ΔT is the change in temperature in Celsius
Let's first convert the volume from liters to kilograms. The density of water is approximately 1 gram/mL, so 50 liters of water would be 50 * 1000 grams.
m = 50 * 1000 grams / 1000 = 50 kg
Now we can calculate the energy:
Q = 50 kg * 4180 J/kg·°C * (100°C - 40°C)
Q = 50 kg * 4180 J/kg·°C * 60°C
Q = 12540000 J
Next, we need to convert the energy from Joules to kilowatt-hours (kWh). Since 1 kWh is equal to 3.6 million Joules, we can divide the energy by 3.6 million:
Energy in kWh = 12540000 J / (3.6 million J/kWh)
Energy in kWh = 3.483 kWh
Finally, we can calculate the cost by multiplying the energy in kWh by the cost per kWh:
Cost = 3.483 kWh * USD 8.0/kWh
Cost = USD 27.864
Therefore, the cost of electrical heating 50 liters of water from 40 degrees Celsius to 100 degrees Celsius at USD 8.0/kWh would be approximately USD 27.864.