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 1.28 pounds of methane (fuel value is 11.97 kcal/g) is used to heat 127.0 kg of water at an initial temperature of 21.5 °C, what is the final temperature? help??

1.28 lbs x 453.59 g/lb = ?grams CH4.

?grams CH4 x (11.97 cal/g) = ? cal heat produced by the l.28 lbs CH4.

?cal = mass H2O x specific heat H2O x (Tfinal-Tintial)
Substitute 127,000 for mass H2O
Solve for Tf
Substitute 21.5 for Ti
Substitute 1 cal/g for specific heat H2O.

I keep getting the wrong answer :/

I did:
1.28lb x 453.59g/lb= 580.5952g CH4
580.5952g Ch4 x 11.97 cal/g= 6949.724544 cal
6964.724544 cal= 127,000 x 1 cal/g x (Tf-21.5)
Final Temp= 21.6*C
but this answer was wrong

nvm! i got it! I forgot to convert 11.97 kcal/g to cal/g

1.28lb x 453.59g/lb= 580.5952g CH4

580.5952g Ch4 x 11.97 cal/g= 6949.724544 cal
6964.724544 cal= 127,000 x 1 cal/g x (Tf-21.5)
You are ok to here. You didn't show your next step but that is the error. Here is your last line.
6964.72 = 127 x 1 x (Tf-21.5)
Then
6964.72 = 127Tf - (127*1*21.5)
6964.72 = 127Tf - 2730.50
6964.72 + 2730.50 = 127Tf
I'll let you take it from here.
Final Temp= 21.6*C

I forgot and didn't turn off the bold and it printed hat last line in bold. Ignore "Final Temp = 21.6"

Well, it seems like you've got quite the hot question there! Let's see if we can heat things up with some calculations.

First, we need to find out how much energy is released from burning 1.28 pounds (which is approximately 0.582 kg) of methane. Since the fuel value of methane is 11.97 kcal/g, we can multiply this by the mass:

Energy released = 0.582 kg * 11.97 kcal/g = 6.957 kJ

Now, we need to use this energy to heat 127.0 kg of water. We'll use the equation:

Energy (in Joules) = mass (in kg) * specific heat capacity * change in temperature

The specific heat capacity of water is approximately 4.186 J/g°C. Let's convert this to kJ/kg°C:

specific heat capacity = 4.186 J/g°C * 0.001 kg/g = 0.004186 kJ/kg°C

Now, let's rearrange the equation to solve for the change in temperature:

change in temperature = Energy (in kJ) / (mass (in kg) * specific heat capacity)

change in temperature = 6.957 kJ / (127.0 kg * 0.004186 kJ/kg°C)

change in temperature ≈ 13.94 °C

Finally, to find the final temperature, we need to add the change in temperature to the initial temperature:

final temperature = initial temperature + change in temperature

final temperature = 21.5 °C + 13.94 °C ≈ 35.44 °C

So, the final temperature of the water would be approximately 35.44 °C. I hope this fiery answer helped to keep you warm!

To solve this problem, we can use the principle of conservation of energy. The energy released by burning 1.28 pounds of methane is equal to the energy absorbed by the water.

First, let's convert the mass of methane from pounds to grams:
1 pound = 453.592 grams
Therefore, the mass of methane is 1.28 pounds * 453.592 grams/pound = 581.2 grams.

Now, let's calculate the energy released by burning the methane:
Energy = Fuel value * Mass
Energy = 11.97 kcal/g * 581.2 grams
Energy = 6,945.564 kcal

Next, we need to calculate the heat absorbed by the water. The formula for heat is:
Heat = mass * specific heat * temperature change

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

The mass of water is 127.0 kg * 1000 g/kg = 127,000 grams.

The initial temperature of the water is 21.5°C.

Let's assume the final temperature of the water is Tf°C.

Using the formula for heat, we can set up the following equation:
6,945.564 kcal = 127,000 grams * 4.186 J/g°C * (Tf°C - 21.5°C)

Now, let's convert kcal to J:
1 kcal = 4.186 kJ = 4.186 * 1000 J
Therefore, 6,945.564 kcal = 6,945.564 * 4.186 * 1000 J

Simplifying the equation:
6,945.564 * 4.186 * 1000 J = 127,000 * 4.186 * (Tf - 21.5) J

Now, divide both sides of the equation by 127,000 * 4.186 to solve for Tf - 21.5:
(6,945.564 * 4.186 * 1000 J) / (127,000 * 4.186) = Tf - 21.5

Calculate the left-hand side of the equation:
LHS = (6,945.564 * 4.186 * 1000 J) / (127,000 * 4.186)

Finally, add 21.5 to both sides of the equation to solve for Tf:
Tf = LHS + 21.5

Calculating Tf will give you the final temperature of the water.