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 1.29 pounds of butane (fuel value is 10.85 kcal/g) is used to heat 122.5 kg of water at an initial temperature of 18.8 °C, what is the final temperature?

Convert 1.29 lbs C4H10 to grams = ?

Then ? g x 10.85 kcal/g = q kcal or 1000q cal.
1000q = mass H2O x specific heat H2O x (Tf-Tinitial)
Solve for Tf.
I estimate the answer is about 71 C.

To solve this problem, we need to use the equation:

\(q = mcΔT\)

Where:
q = heat energy (in calories or joules)
m = mass of the substance (in grams or kilograms)
c = specific heat capacity (in calories/gram/°C or joules/gram/°C)
ΔT = change in temperature (in °C or K)

First, let's find the amount of heat energy released by burning 1.29 pounds of butane. We'll convert the mass from pounds to grams:

1.29 pounds = 1.29 * 454 grams (1 pound = 454 grams)
= 585.06 grams (rounded to the nearest hundredth)

Next, we need to convert the fuel value from kcal/g to calories/gram:

Fuel value = 10.85 kcal/g * 1000 cal/1 kcal
= 10850 cal/g

Now we can calculate the heat energy released:

q = 585.06 grams * 10850 cal/g
= 6,35,43,430 cal

Now, let's find the heat energy required to raise the temperature of 122.5 kg (or 122,500 grams) of water from 18.8 °C to the final temperature.

Since the specific heat capacity of water is approximately 1 calorie/gram/°C, we can use the equation:

q = mcΔT

Where:
q = 6,35,43,430 cal (heat energy)
m = 122,500 grams (mass of water)
c = 1 cal/g/°C (specific heat capacity of water)
ΔT = final temperature - initial temperature = ΔT

Rearranging the equation, we can solve for ΔT:

ΔT = q / (mc)

ΔT = 6,35,43,430 cal / (122,500 g * 1 cal/g/°C)
= 6,35,43,430 cal / 122,500 cal/°C
= 51.89 °C

Finally, we can find the final temperature by adding ΔT to the initial temperature:

Final temperature = Initial temperature + ΔT
= 18.8 °C + 51.89 °C
= 70.69 °C

Therefore, the final temperature after using the energy released from burning 1.29 pounds of butane to heat 122.5 kg of water is approximately 70.69 °C.