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 1.30 pounds of methane (fuel value is 11.97 kcal/g) is used to heat 122.0 kg of water at an initial temperature of 21.1 °C, what is the final temperature?

Question

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 1.30 pounds of methane (fuel value is 11.97 kcal/g) is used to heat 122.0 kg of water at an initial temperature of 21.1 °C, what is the final temperature?

Answer 1

1.30 pounds x 453.6 g/lb = ? grams.

11.97 kcal/g x ?g = # kcal and that times 1000 = # calories = q
q = mass H2O in g x specific heat H2O x (Tfinal-Tinitial).
Subsitute and solv for Tfinal.

Answer 2

To find the final temperature, we can use the principle of conservation of energy. The energy released by burning the methane will be used to heat the water, so we can equate the two energy values.

First, let's convert the mass of methane from pounds to kilograms. We know that 1 pound is approximately equal to 0.454 kilograms. Therefore, 1.30 pounds is equivalent to 1.30 * 0.454 = 0.5912 kilograms.

Next, we need to determine the energy released by burning the methane. The fuel value provided is 11.97 kcal/g. To find the total energy released, we multiply the fuel value by the mass of the methane:

Energy released = fuel value * mass
Energy released = 11.97 kcal/g * 0.5912 kg

Now let's convert the units to match the units of energy required to heat the water. Since 1 calorie (cal) is equal to 4.184 joules (J), we can convert the energy released from kcal to J:

Energy released = (11.97 kcal/g * 0.5912 kg) * 4.184 kJ/cal

Next, we need to find the energy required to heat the water. We can use the equation:

Energy required = specific heat capacity * mass of water * change in temperature

The specific heat capacity of water is approximately 4.184 J/g°C. The mass of water is given as 122.0 kg, and the initial temperature is 21.1 °C.

Now we can rearrange the equation to solve for the change in temperature:

Change in temperature = Energy released / (specific heat capacity * mass of water) + initial temperature

Substituting the values into the equation, we get:

Change in temperature = (Energy released) / (4.184 J/g°C * 122.0 kg) + 21.1 °C

Finally, we can use this equation to calculate the change in temperature (final temperature - initial temperature):

Final temperature = Change in temperature + initial temperature

Substituting the values into the equation, we can find the final temperature.