Principles of heat: How many kilograms of water can be evaporated at 100 degrees Celsius by the combustion of 470 litres of fuel oil whose heat of combustion is 37 MJ/Litre
16.393kg
To determine the number of kilograms of water that can be evaporated, we need to consider the heat of combustion and the specific heat capacity of water. Here's how you can calculate it:
Step 1: Convert the volume of fuel oil from liters to cubic meters.
Since 1 liter is equal to 0.001 cubic meters, we can convert 470 liters to cubic meters as follows:
470 liters * 0.001 = 0.47 cubic meters.
Step 2: Calculate the total energy released from the combustion of the fuel oil.
To find the total energy released, we multiply the volume of fuel oil by its heat of combustion.
Total energy released = volume of fuel oil * heat of combustion
In this case, the volume of fuel oil is 0.47 cubic meters, and the heat of combustion is given as 37 MJ/Liter. We can convert the MJ/Liter to Joules/m^3 by multiplying it by 1,000,000 (since 1 MJ = 1,000,000 J):
Heat of combustion = 37 MJ/Liter * 1,000,000 J/MJ = 37,000,000 J/Liter
Now we can calculate the total energy released:
Total energy released = 0.47 cubic meters * 37,000,000 J/Liter
Step 3: Convert the total energy released to the amount of water evaporated.
To convert the energy to the number of kilograms of water evaporated, we need to consider the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/(g °C).
The formula to calculate the amount of water evaporated is:
Mass of water evaporated = Total energy released / (specific heat capacity of water * temperature change)
In this case, the temperature change is the difference between the boiling point of water (100 degrees Celsius) and the initial temperature of the water, which is assumed to be 0 degrees Celsius.
Mass of water evaporated = Total energy released / (4.18 J/(g °C) * (100 - 0) °C)
Now you can substitute the values and calculate:
Mass of water evaporated = [0.47 cubic meters * 37,000,000 J/Liter] / (4.18 J/g°C * 100)
Note that the resulting mass will be in grams. If you want the mass in kilograms, you can divide the final value by 1000.
By following these steps and performing the calculations, you can determine the number of kilograms of water that can be evaporated by the combustion of the given volume of fuel oil.