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?!!

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 1.28 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?!!

Answer 1

To solve this problem, we can use the concept of heat transfer:

1. Calculate the total energy obtained from burning 1.28 pounds of methane:
Total energy = Mass of methane * Fuel value
= 1.28 pounds * (11.97 kcal/g) * (453.6 g/pound) [Note: 1 pound = 453.6 grams]

2. Convert the mass of water from kilograms to grams:
Mass of water = 127.0 kg * 1000 g/kg

3. Calculate the heat absorbed by water:
Heat absorbed = Mass of water * Specific heat of water * Change in temperature

Since we want to find the final temperature, we can rearrange the equation as:
Change in temperature = Heat absorbed / (Mass of water * Specific heat of water)

4. Calculate the final temperature:
Final temperature = Initial temperature + Change in temperature

Let's calculate the values step by step:

Step 1:
Mass of methane = 1.28 pounds = 1.28 * 453.6 g = 581.248 g
Total energy = 581.248 g * 11.97 kcal/g

Step 2:
Mass of water = 127.0 kg * 1000 g/kg

Step 3:
To calculate the heat absorbed, we need to know the specific heat of water. The specific heat of water is approximately 4.18 J/g°C.

Heat absorbed = Mass of water * Specific heat of water * Change in temperature

Step 4:
Change in temperature = Heat absorbed / (Mass of water * Specific heat of water)

Final temperature = Initial temperature + Change in temperature

Let's calculate the values to find the final temperature:

Answer 2

To find the final temperature, we can use the concept of specific heat capacity and the equation:

q = mcΔT

Where:
- q is the amount of heat energy transferred
- m is the mass of the substance
- c is the specific heat capacity of the substance
- ΔT is the change in temperature

First, let's calculate the amount of heat energy released by burning 1.28 pounds of methane.

1.28 pounds is approximately 0.581 kilograms (since 1 pound is equal to 0.4536 kilograms).

Next, convert the fuel value from kcal/g to kcal/kg:

11.97 kcal/g = 11.97 kcal/g * 1000 g/kg = 11970 kcal/kg

To find the total amount of heat energy released, multiply the mass of methane burned by its fuel value:

q_methane = 0.581 kg * 11970 kcal/kg = 6946.57 kcal

Now, we need to calculate the amount of heat energy required to heat 127.0 kg of water from 21.5 °C to the final temperature:

q_water = mcΔT

The specific heat capacity of water (c) is approximately 4.186 J/g·°C or 4.186 kcal/kg·°C.

Converting the specific heat capacity to kcal/kg·°C:

4.186 kcal/kg·°C

ΔT can be calculated with the equation:

ΔT = q_water / (mc)

Rearranging the equation to solve for ΔT:

ΔT = q_water / (mc)

Substituting the known values:

ΔT = (6946.57 kcal) / (127.0 kg * 4.186 kcal/kg·°C)

Calculating ΔT:

ΔT ≈ 12.971 °C

Now, to find the final temperature (T_f), we add ΔT to the initial temperature (T_i):

T_f = T_i + ΔT

T_f = 21.5 °C + 12.971 °C

T_f ≈ 34.471 °C

Therefore, the final temperature of the water is approximately 34.471 °C.