Hey I'm new to the forums, but I could really use some help with a problem. My school does a senior design project where we design and build some prototype system. My team has a client that wants an internal cooling device through inhalation. I'm the only team member who has had experience with thermodynamics.

So I made a few assumptions to actually be able to do this:

1. Heat generated by metabolism is equal to heat lost to atmosphere.( Qmetabolism and Qloss through skin)

2. change in energy over change in time is constant (dE/dt = deltaE/delta t)

Our client wanted us to have 2 control volumes.

The lungs are control volume I and is an open system.

The body is control volume II and is a closed system.

I'm unsure about how to use Conservation of energy to find this relationship. I know what I am probably messing up is the difference in the closed and open system.

I can also give values and constants if necessary although I would prefer to do everything in symbol form first.

Any help would be greatly appreciated!

Whenever you have a tricky problem like this, start with something very simple and then make it more complicated later after you have some solutions.

For example, the lungs can be approximated by a container with a constant temperature equal to the ambient temperature. The rest of the body can then be approximated by another container with the typical dimensions of a humanoid, which surround the first container. Since the question requires the lungs to be an open system, you'll need to track the amount of energy entering the lungs (by mass influx) and energy leaving the lungs (through mass outflux). You can make some assumptions to begin with about the inhalation and exhalation, such as, for example, constant, time-independent, net energy outflux. For the body, since it is a closed system, you can consider it as adiabatic to the outside air (no heat loss through the skin) so the only temperature exchange is between the lungs and the body. You can also assume thermal equilibrium.

Then, for the lungs, you'll have something like this:

\(\displaystyle E_{exhale} = E_{conv}\)

\(\displaystyle E_{exhale} = hA(T_{body} - T_{amb})\)

and for the body

\(\displaystyle E_{metabolism} = E_{exhale}\)

This will allow you to calculate the metabolism required to equal the net energy loss. Later, if you want, you can consider time-dependent terms and other heat transfer mechanisms (like conduction using Fourier's law).