## 6.4 Problem Set

1. Using the data in Figure 6.1, show that the First Law holds for the earth’s surface and the earth’s atmosphere.

2. In the module we used the First Law to calculate the change in temperature with elevation. With this knowledge what generalizations can you suggest about differences in communities with elevation and latitude? On a graph of elevation versus latitude plot lines of constant temperature (mean annual temperature). Assume 0° latitude is 26°C and each degree toward the poles lowers the mean annual temperature 0.5°C. Do this for wet and dry lapse rates. How does this compare with real data?

3. Choose any organism, part of an organism or specific environment that an organism frequents from the four examples given at the beginning of the module titled “The First Law of Thermodynamics for Ecosystems.” Define the system, surroundings, and write down the First Law heat energy balance for your system. How meaningful is your system biologically? What terms from the general heat flux equation are most important for your system? How does the choice of your system influence the biological interpretations you can make?

4. Repeat exercise 2 for a system of your own choice.

5. Organisms commonly exchange mass with their environment during respiration and feeding. For homeotherms this usually involves a net loss of energy because the matter taken in is warmed to body temperature before it is expelled.

1. As a first example consider respiration exchange of a 0.5 kg bird. Calder (1975) gives the frequency in breaths $$s^{-1}$$ as $$0.2867 M^{-0.31}$$ and the tidal volume ($$m^3$$) as $$13.2\times 10^{-6} M^{1.08}$$ where $$M$$ is in kg. If the bird warms the air 30°C, what is the net heat loss in watts?

2. Assume a horse drinks 10 gallons of water at 20°C and urinates it at 38°C during the course of a day. What is the loss in watts?

1. Imagine that you have been retained as an environmental consultant to advise state officials in the Department of Ecology about management problems. The Department wishes to update the Timber Harvesting Practices Act. They have asked you to make some general statements about the effects of timber cutting of the spawning grounds of the salmonoid fish, specifically discussing the relative importance of siltation, stream flow and the elevation of water temperatures. In stream sections where water temperature changes are most important, discuss which factors of the physical environment must be considered to understand the thermal balance of the stream.

2. In the module titled “The First Law of Thermodynamics for Ecosystems” I used a problem to introduce the idea that potential ($$E_p$$) and kinetic ($$E_k$$) energies could be included in the First Law. Imagine you are studying the locomotion mechanics and energetics of the rhea, a bipedal bird. Write down an energy conservation equation to identify the three components of the mechanical work (the rhea can be thought of as a point mass analogous to a pendulum). How would you compute these components? Discuss their relative importance. How might you measure the efficiency of locomotion? Of the initial chemical energy used which could be measured by oxygen consumption, how much represents work done by the organism? Where does the other energy go?

3. In the last section of the module we commented on the interaction of regulation of body temperature and the acquisition of food energy. Describe the steps necessary to convert energy in the environment to usable chemical energy for the body. During each step of the process what is the importance of the thermal environment for a poikilotherm and a homeotherm?