The amount of energy released by burning a fuel source, measured in energy per mass, is called the fuel value. If all the energy obtained from burning 1.25 pounds of propane (fuel value is 11.09 kcal/g) is used to heat 123.0 kg of water at an initial temperature of 18.1 °C, what is the final temperature?
mass fuel = 1.25lbs x (453.6 g/lb) = ?
q = ?g fuel x 11.09 kcal/g
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
specific heat H2O must be used in kcal/g.
To solve this problem, we need to calculate the total energy released by burning 1.25 pounds of propane first. Then we can use this energy to determine the change in temperature of the water.
Step 1: Convert the mass of propane from pounds to grams.
To convert pounds to grams, we'll multiply the given mass of propane (1.25 pounds) by the conversion factor: 1 pound = 453.592 grams.
1.25 pounds * 453.592 grams/pound = 567.99 grams
Therefore, the mass of propane is approximately 567.99 grams.
Step 2: Calculate the total energy released by burning the given mass of propane.
The fuel value given for propane is 11.09 kcal/gram.
Total energy released = Mass of propane * Fuel value
Total energy released = 567.99 grams * 11.09 kcal/gram
To find the energy in kilojoules (kJ), we'll convert kcal to kJ using the conversion factor: 1 kcal = 4.184 kJ.
Total energy released = (567.99 grams * 11.09 kcal/gram) * (4.184 kJ/kcal)
Step 3: Calculate the heat absorbed by the water.
The heat absorbed by the water is equal to the total energy released.
Heat absorbed = Total energy released
Step 4: Calculate the change in temperature of the water.
The heat absorbed by the water is given by the equation:
Heat absorbed = Mass of water * Specific heat of water * Change in temperature
Rearranging the equation to solve for the change in temperature:
Change in temperature = Heat absorbed / (Mass of water * Specific heat of water)
Given:
Mass of water = 123.0 kg (Notice that the mass must be in kilograms, so we don't need to convert it.)
Specific heat of water = 4.186 J/g°C (This is the specific heat capacity of water.)
Change in temperature = Heat absorbed / (Mass of water * Specific heat of water)
Change in temperature = Heat absorbed / (123.0 kg * 103 J/kg°C)
Finally, substituting the values and calculating the change in temperature:
Change in temperature = (Total energy released) / (123.0 kg * 103 J/kg°C)
Therefore, the final temperature can be calculated by adding the change in temperature to the initial temperature of 18.1 °C.