8-1. Use the "Random Walk" Mathematica notebook to simulate the motion of a molecule of 2 - Furylmethanethiol diffusing from a coffee cup at the origin. Collect values for the distance travelled from the origin versus time, and use the Gaussian relation between average distance and time to compute the diffusion constant. Compare with the value computed using the equipartition theorem. How does your accuracy depend on the number of walks?
8-2. Increased energy increases the probability of collision and energy of collision, which in turn raises reaction rates. Using the "Boltzmann Example" Mathematica notebook, graph the Boltzmann Distribution (probability as a function of temperature) for each bond below and identify the temperature at which each destabilizes by choosing an appropriate cut-off in the graph (ie., when the probability reaches 0.5).
| Bond | Energy (kcal / mol) |
|---|---|
| C-C | 83 |
| C-N | 70 |
| C-O | 84 |
| C-H | 99 |
| C=C | 146 |
| C==C (triple bond) | 212 |
| O-H | 110 |
| C=O | 170 |
| N-H | 103 |
| H bond in H 2 O | 4.5 |
| H bond | .5 - 12 |
(1 cal = 4.186 J)
8-3 through 8-7. Compute the membrane potential using both the Nernst and Goldman Equations for the following cell types:
| type | cNa+in | cK+in | cCl-in |
|---|---|---|---|
| skeletal muscle | 12 | 150 | 4 |
| cardiac muscle | 7 | 134 | 4 |
| liver | 3 | 148 | 16 |
| thyroid | 42 | 147 | 19 |
| erythrocytes | 19 | 136 | 78 |
| (interstitial fluid | 145.1 | 4.1 | 115.7) |
Compute the Nernst equation for potassium. Concentrations are in milliequivalents per liter. PK = PCl = 4.5 x 10 - 6 cm / s, and PNa = 9 x 10 - 8 cm / s. Assume body temperature (37 C).
If you would like to do these problems without a calculator, note that e is approximately 2 1.44; this means that ln(x) = 0.7 log 2 (x), and you can use the approximations (with base 2 instead of e) you tried in chapter 7.
8-8. What would your weight loss in water be if your body lost 2000 Cal per day solely to evaporation?
8-9. Assume you have a surface area of 2 square meters and the ambient temperature is 22 C. Compute the rate of heat lost due to radiation for skin temperatures of 28 C (resting) and 36 C (after active exercise).
8-10. In the scenario in problem 8-9, compute the loss due to conduction through the private climate (use k air).
8-11. In a diving environment, the nitrogen in air is replaced by helium. Look up the conductivity of helium and repeat problem 8-10 for this scenario. If the conduction rate must be limited to 20 W (for reasons of comfort), what is the minimum ambient temperature? What is the minimum ambient temperature if the conductivity increases by a factor of five when diving?
8-12. What is the rate of perspiration required to lose 200 W?
8-13. Evaporation is very ineffective on humid days. What would be the increase in a 70 kg runner's body temperature after a half hour run when he retained 30 W of heat?
8-14. The clothing of a drenched hiker absorbed about a liter of water. At a body heat production rate of 4 Cal / minute, how long would it take to evaporate this water? Use (look up) the latent heat of vaporization at 25 C. If all of this energy came from the hiker's body, what would be his body temperature when dry (assume that his mass is 70 kg)?
In the problems below, use normal body temperature when necessary.
8-15. Fat is a more efficient storage mechanism per unit mass than carbohydrates for long term storage. Show that this is true by comparing the energy released in the form of ATP per gram of the fatty acid palmitate (C 16 H 32 O 2) with that of glucose. One molecule of palmitate produces 131 molecules of ATP.
8-16. Mammalian skeletal muscle cells use 1 mmol of ATP per minute per gram of muscle tissue during contraction (typical initial concentration is 5 micromols / g). How long can the muscle stay contracted using just ATP?
8-17. If ATP is being supplied by aerobic respiration, how many milliliters of oxygen must be supplied to the cells per minute per gram of tissue in order to sustain the contraction after the initial ATP is used up? The density of oxygen is 1.43 g / L.
8-18. In the last problem, what is the rate of weight loss per gram of tissue, assuming that all of the carbon dioxide and water is exhaled?
8-19. Compute the changes in free energy and entropy, and the efficiency, for glycolysis.
8-20. Repeat the last problem for electron transport, taking into account the fact that there are ten NADH transport chains for every two FADH 2 chains.
8-21. Verify the change in entropy for aerobic respiration by adding up the changes in entropy for glycolysis, the TCA cycles and the electron transport chains.
Assume that photosynthesis takes place at room temperature.
8-22. 2.5 x 10 18 cal / s (1.94 cal / cm 2 s) is supplied to the Earth's atmosphere by the Sun. Plants use 5 x 10 16 g of carbon to make glucose each year. What percentage of the energy supplied to the Earth by the Sun is used photosynthetically?
8-23. The growing season for sugar beets in Wisconsin is May 15 to September 1, with an average of 15 hours of daylight per day. If 72 % of the sunlight in the last problem reaches the ground and sugar beets are 20% sucrose (equivalent to glucose for a photosynthesis problem), what is the maximum yield per hectare annually? Remember to use the results of the last problem!
8-24. Compute the total entropy change of one glucose molecule from respiration to regeneration via photosynthesis.
8-25. From the point of view of you as a complete organism, your efficiency increases when you are on a diet (as long as your activity does not decrease). By what percent must you decrease your caloric intake if you want to increase your efficiency by 5 %?
8-26. Normal potassium concentrations in and outside of a mammalian axon are around 150 and 5 mmols/liter, respectively. Assuming that the axon will only function with rest potentials within a range of plus or minus 20 mV from normal, compute the percentage tolerances of intracellular potassium concentration. Assume that the potassium concentration in the interstitial fluid remains unchanged (why might that be?). What symptoms occur as intracellular potassium levels deviate from normal?
8-27. Suppose that you exercise for 45 minutes each day, and that during that period your body must lose 12 kcal/minute in excess heat. If your skin temperature is 36.5 C, and you lose 0.6 liters of water in exhalation and sweat during the 45 minutes, what is the ambient temperature necessary to maintain a static internal temperature when the air is still? when the air speed is 10 km/hr? Use the formula for surface area from Chapter 3 to compute your surface area, and estimate the percentage that is exposed during your exercise. You may ignore radiation for the purpose of this exercise, although it is not negligible; it complicates the algebra enormously!
8-28. What is the percentage decrease in the conductive heat current when you wear a 1 cm thick down jacket in the winter? Assume that there is a 5 mm air space between your skin and the lining of the coat, and that the jacket covers one half of your body surface.
8-29. What is the change in free energy in Photosystem II? If you cannot find the free energy of NADPH, assume that it is the same as NADH and discuss the ramifications of that assumption.
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©1996, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.
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