# I'm inventing my own physics problem for extra credit thermodynamics and fluids

• ginale
In summary, the conversation discusses a man falling into a tank at 40 degrees Celsius and his body temperature of 98.6 degrees Fahrenheit. The question of whether the man will freeze to death and at what temperature that happens is raised, along with asking if his final body temperature can be determined if he is not rescued in 10 minutes. The conversation also mentions equations for temperature conversion and heat transfer, and suggests a related problem involving estimating the rate of heat removal from the body.
ginale
1. A man falls into a tank at 40 degrees C. His body temperature is 98.6 degrees Fahrenheit. I want to ask if the man will freeze to death, but I don't know at what temperature that happens. Can I ask them to figure out what his final body temperature is, if say he doesn't get rescued in 10 mins? Do I need to provide more information? I can always go off in a completely different direction...

2. Tc = (5/9)*(Tf-32)
Q=mL
Q=mCdeltaT

ginale said:
1. A man falls into a tank at 40 degrees C. His body temperature is 98.6 degrees Fahrenheit. I want to ask if the man will freeze to death, but I don't know at what temperature that happens. Can I ask them to figure out what his final body temperature is, if say he doesn't get rescued in 10 mins? Do I need to provide more information? I can always go off in a completely different direction...

2. Tc = (5/9)*(Tf-32)
Q=mL
Q=mCdeltaT

First off, do you mean the tank of water is 40º Fahrenheit? Water at 40º C (104º F) would be mighty uncomfortable, but you won't freeze to death in it...

In any case, hypothermia is a rather complicated physiological condition. People have been recovered with body core temperatures that had fallen below 65º F and been revived successfully. Likewise, the time of fatal exposure to near-freezing water varies pretty widely. But I'd say that ten minutes is rarely lethal, though half an hour generally is.

The difficulty in introducing time into your problem is that you need to include information about the rate at which heat is being lost from the person's body. Has your physics course covered problems in conductive heat transfer at all? The thermal equation you've given would need to be differentiated implicitly with respect to time to create a rate equation relevant to your problem. Have students in the course done problems like that before? You would have to provide at least a crude model of how heat would be lost from the body in those circumstances to give the problem enough of a "closed form" for students to solve it.

A related sort of problem would be to have students solve for the rate at which heat is removed from the body by perspiration. You'd need estimates for the surface area of the body (assuming perspiration is uniform over the surface -- which it isn't, really), a rate at which water is leaving the pores everywhere, and the latent heat of vaporization of water at skin temperature (around 85º F -- you could google up a table for such data, I believe).

You could even extend the problem to estimate how fast heat is also being removed by breathing, using the rate at which air at body core temperature (pretty much 98.6 F) is warmed and expelled; you could also include the water vapor content in the breath, which is probably picking up most of the heat. The results could be compared with the average rate at which metabolism generates heat in the body (around 100 W -- have them find this too!). The calculations still require certain assumptions, but I think it's a bit more tractable than trying to model the whole body. Just a suggestion...

Last edited:

Hello! It sounds like you have a great idea for a physics problem. Let's break it down and see what information we need to provide in order to make it solvable.

First, we have a man falling into a tank at a temperature of 40 degrees Celsius. We also know his body temperature is 98.6 degrees Fahrenheit. In order to determine if the man will freeze to death, we need to know the freezing point of water, which is 0 degrees Celsius or 32 degrees Fahrenheit. This means that the man's body temperature is higher than the freezing point of water, so he will not freeze to death.

Next, you want to know the man's final body temperature if he is not rescued in 10 minutes. In order to calculate this, we need to know the specific heat capacity of the man's body, which is the amount of energy needed to raise the temperature of one gram of the body by one degree Celsius. We also need to know the mass of the man's body. With this information, we can use the equation Q=mCdeltaT to calculate the change in the man's body temperature over the course of 10 minutes. This will give us his final body temperature.

To make this problem more challenging, you can also include the temperature of the tank and the specific heat capacity of the water in the tank. This will affect the rate of heat transfer between the man's body and the water, and therefore his final body temperature.

As for your third question, it's always a good idea to start with a clear and concise statement of the problem, including all the necessary information. This will help guide the students in solving the problem and prevent any misunderstandings. Additionally, you can include any additional information or variables that you think would make the problem more interesting or challenging.

I hope this helps guide you in writing your physics problem. Good luck!

## 1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the study of heat and its relationship to other forms of energy. It also focuses on the behavior of gases, liquids, and solids under different conditions.

## 2. How does thermodynamics relate to fluids?

Thermodynamics is closely related to fluids because it helps us understand the behavior of fluids, such as liquids and gases, in various systems. This includes how they transfer heat and energy, and how they respond to changes in temperature and pressure.

## 3. What is the difference between the first and second laws of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. The second law of thermodynamics states that the total entropy (disorder) of a closed system will always increase over time.

## 4. How can thermodynamics be applied in real life?

Thermodynamics has numerous applications in our daily lives, such as in the design of engines, refrigerators, and air conditioners. It also helps us understand weather patterns, the functioning of our bodies, and the production of electricity.

## 5. How can I use thermodynamics and fluids to create my own physics problem for extra credit?

There are many ways to incorporate thermodynamics and fluids into a physics problem, such as calculating the work done by a fluid in a system, analyzing the efficiency of a heat engine, or determining the change in entropy of a gas during a process. The key is to apply the principles and equations of thermodynamics to a specific scenario or system, and then create a problem that requires students to use their understanding of these concepts to solve it.

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