How Do You Solve Complex Thermal Energy Problems?

[ilovemoney518]

Thermal Energy Problem HELP PLEASE!

Hi guys I have these 2 thermal energy problems that I keep getting wrong answer, I really want to know the answer and the way to solve it. Thank u very much!


1. The average thermal conductivity of the walls (including windows) and roof of a house in Figure P11.32 is 4.8 10-4 kW/m°C, and their average thickness is 20.0 cm. The house is heated with natural gas, with a heat of combustion (energy given off per cubic meter of gas burned) of 9300 kcal/m3. How many cubic meters of gas must be burned each day to maintain an inside temperature of 24.5°C if the outside temperature is 0.0°C? Disregard radiation and loss by heat through the ground.



2. When you jog, most of the food energy you burn above your basal metabolic rate (BMR) ends up as internal energy that would raise your body temperature if it were not eliminated. The evaporation of perspiration is the primary mechanism for eliminating this energy. Determine the amount of water you lose to evaporation when running for 30 minutes at a rate that uses 400 kcal/h above your BMR. (That amount is often considered to by the "maximum fat-burning" energy output.) The metabolism of 1 gram of fat generates approximately 8.5 kcal of energy and produces approximately 1 gram of water. (The hydrogen atoms in the fat molecule are transferred to oxygen to form water.) What fraction of your need for water will be provided by fat metabolism? (The latent heat of vaporization of water at room temperature is 2.5 106 J/kg.)

For the first problem the answer I got is 119.96. But it was wrong. I can't afford to try more because I only have 3 chances and I am totally lost. The second problem I have no clue, could anyone guide me a little?

 

[Astronuc]

What equation are you using for problem 1? Please show some work.

On two - on is asked to "Determine the amount of water you lose to evaporation when running for 30 minutes at a rate that uses 400 kcal/h above your BMR." From that one can determine total kcal.

Then use "The metabolism of 1 gram of fat generates approximately 8.5 kcal of energy and produces approximately 1 gram of water." find production of water from fat metabolism.

The total water loss (from evaporation) is found using "The latent heat of vaporization of water at room temperature is 2.5x10⁶ J/kg."

 

[quicknote]

Hi there! I can definitely understand your frustration with these thermal energy problems. However, don't give up just yet! Let's break down each problem and see if we can figure out the solutions together.

In the first problem, we are given the thermal conductivity of the walls and roof of a house, as well as the heat of combustion of natural gas. We are asked to find out how many cubic meters of gas must be burned each day to maintain a certain inside temperature. This problem involves using the equation Q = kAΔT/L, where Q is the heat transfer, k is the thermal conductivity, A is the area, ΔT is the temperature difference, and L is the thickness. In this case, we are given all the values except for A. We can find A by multiplying the length and width of the house. Once we have that, we can plug in all the values and solve for Q. Then, we can divide Q by the heat of combustion to find out how many cubic meters of gas are needed each day.

For the second problem, we are looking at the amount of water lost through evaporation during exercise. We are given the energy output and the amount of water produced by the metabolism of fat. We can use these values to calculate the amount of water lost during a 30-minute jog. The key here is to convert the energy output from kcal to J, and then use that to find the amount of water lost using the equation Q = mLv, where Q is the heat transfer, m is the mass of water, and Lv is the latent heat of vaporization. Once we have the amount of water lost, we can compare it to the total water needed by the body during exercise to find the fraction provided by fat metabolism.

I hope this helps guide you in solving these problems. Remember, don't give up and keep practicing! Science can be challenging, but with determination and practice, you can definitely master it. Good luck!