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 butane (fuel value is 10.85 kcal/g) is used to heat 120.0 kg of water at an initial temperature of 21.2 °C, what is the final temperature?

1.25 pounds x 453.6 g/pound = ?grams

?grams x 10.85 kcal/g = x kcal
x kcal x 1000 cal/kcal = 120,000 g H2O x specific heat H2O (cal/g) x (Tfinal-Tinitial)

DrBob,

started to do this equation, but am unsure if degrees Celcius needs to be converted to Kelvins in this instance before proceeding with the problem. Does it need to be converted, or is that just for calculation in Gas Laws?

To find the final temperature, we can use the equation:

Energy released from burning the butane = Energy absorbed by water

First, let's find the energy released from burning 1.25 pounds (0.567 kg) of butane:

Energy released = mass of butane x fuel value
= 0.567 kg x 10.85 kcal/g x 1000 g/kg
= 6,143.95 kcal

Now, let's find the energy absorbed by water:

Energy absorbed = mass of water x specific heat x change in temperature

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

Converting the mass of water to grams:
mass of water = 120.0 kg x 1000 g/kg
= 120,000 g

Using the equation:
6,143.95 kcal = 120,000 g x 4.186 J/g°C x change in temperature

Simplifying:
6,143.95 kcal = 502,320 J/°C x change in temperature

Divide both sides by 502,320 J/°C to solve for the change in temperature:

change in temperature = 6,143.95 kcal / 502,320 J/°C
≈ 12.23 °C

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

Final temperature = initial temperature + change in temperature
= 21.2 °C + 12.23 °C
≈ 33.43 °C

Therefore, the final temperature of the water would be approximately 33.43 °C.

To find the final temperature of the water, we can apply the principle of energy conservation. We need to calculate the amount of energy released by burning 1.25 pounds of butane and then equate that energy to the energy needed to heat the water.

Step 1: Convert pounds to kilograms
1 pound is approximately equal to 0.4536 kg. Therefore, 1.25 pounds is equal to 1.25 * 0.4536 kg = 0.567 kg.

Step 2: Calculate the energy released by burning the butane
The fuel value of butane is given as 10.85 kcal/g. Since we have 0.567 kg of butane, we need to convert it to grams: 0.567 kg * 1000 g/kg = 567 g.
The energy released can be calculated as energy = mass * fuel value = 567 g * 10.85 kcal/g.

Step 3: Convert the energy released to joules
To use the energy in the following calculations, we need to convert it from kilocalories (kcal) to joules (J). 1 kcal is approximately equal to 4184 J. Therefore, the energy released is 567 g * 10.85 kcal/g * 4184 J/kcal.

Step 4: Determine the energy needed to heat the water
The specific heat capacity of water is 4.184 J/g·°C. We need to calculate the energy needed to raise the temperature of 120.0 kg of water from 21.2 °C to the final temperature.

ΔE = m * c * ΔT
Where:
ΔE = Energy needed (in joules)
m = mass of water (in grams)
c = specific heat capacity of water (in J/g·°C)
ΔT = change in temperature (final temperature - initial temperature)

Since mass is given in kilograms, we need to convert it to grams:
mass = 120.0 kg * 1000 g/kg = 120000 g.

Substituting the values into the equation:
ΔE = 120000 g * 4.184 J/g·°C * (final temperature - 21.2 °C)

Step 5: Equate the two energies and solve for the final temperature
Set the energy released equal to the energy needed to heat the water:
567 g * 10.85 kcal/g * 4184 J/kcal = 120000 g * 4.184 J/g·°C * (final temperature - 21.2 °C)

Simplify the equation:
567 * 10.85 * 4184 = 120000 * 4.184 * (final temperature - 21.2)

Solve for the final temperature:
(final temperature - 21.2) = (567 * 10.85 * 4184) / (120000 * 4.184)
final temperature = (567 * 10.85 * 4184) / (120000 * 4.184) + 21.2

Evaluate the expression to find the final temperature.