- Calculate the drag force on objects and calculate the rate of energy dissipation caused by the drag force. 
- Explain how energy dissipation during a collision can be maximized in order to reduce impact forces and prevent injuries. 
- Compare and contrast thermal energy, temperature, and heat. 
- Calculate maximum possible efficiencies for heat engines and explain how the Second Law of Thermodynamics limits that efficiency .
1) A swimmer is moving through water at a constant speed of 0.75 m/s. The drag coefficient for a human in the prone position is roughly 0.25.
a) Calculate the drag force on the swimmer. You will need to estimate the cross-sectional area of a human moving horizontally through the water. You may use measurements of your own body. You also will need to look up the of water in standard units. Be sure to cite your source.
b)What is the size and direction of the average force applied by the swimmer to the water during throughout their swimming stroke?
c) At what rate is energy dissipated by the drag force (dissipation power).
d) If the person is 15% mechanically efficient at swimming, what is their metabolic rate?
e) What is their thermal power?
2) Explain why bicycle helmets are designed as a hard, but very thin shell surrounding foam. Why is the foam brittle instead instead of spongy?
3) A person jumps into a frigid mountain lake. Considering the person and the lake, compare their values of temperature, thermal energy, and heat and be sure to explain whether each value is positive or negative and how you know.
4) Human body temperature is 98.6 °F.
a) Convert this to Celsius.
b) Convert body temperature to .
4) The mitochondria within our cells serve as the powerplants of the body by hosting the the biochemical processes of respiration and ATP synthesis. Data from a recently study, which has yet to be widely reproduced, suggest that the mitochondra operate at temperatures as high as 50 °C . In that case, we could attempt to analyze the mitochondria as heat engines operating between 50 °C and surrounding body temperature at 37 °C.
a) What is the maximum possible efficiency of such a heat engine (don’t forget to convert to Kelvin)?
b) Why is there a maximum limit on the efficiency of such a heat engine?
c) How does the efficiency you calculated compare to the actual efficiency of the body? Give a rough estimate in the form of a ratio.
The value you found was much less than the actual efficiency of the body because the body is not operating as a classic heat engine would. A heat engine would combust fuel to produce concentrated thermal energy (indicated by high temperature) and then transfer that thermal energy into mechanical work and exhaust heat. The exhaust heat reduces the energy concentration (increases entropy) to ensure that 2nd Law is satisficed. However, the process of combusting the fuel in the first place must also follow the 2nd law of thermodynamics, so the entropy in the hot combustion gasses is higher than in the unburned fuel. That means increasing the entropy even further requires quite a bit of heat to be exhausted, which lowers efficiency. Your body on the other hand doesn’t use thermal energy as input. Instead, with the help of enzymes, your body employs non-combustion chemical reactions to convert chemical potential energy in fuel to work and heat without the need for combustion of the fuel. Without the intermediate combustion raising the entropy before the engine even works it becomes “easier” to ensure that entropy still increases overall, meaning that less heat must be exhausted to satisfy the 2nd Law. Acting as a “chemical engine” your body is much more efficient than a heat engine operating at biological temperatures.
- Chrétien D, Bénit P, Ha HH, Keipert S, El-Khoury R, Chang YT, Jastroch M, Jacobs HT, Rustin P, Rak M. Mitochondria are physiologically maintained at close to 50 °C. PLoS Biol. 2018 Jan 25;16(1):e2003992. doi: 10.1371/journal.pbio.2003992. PMID: 29370167; PMCID: PMC5784887. ↵
- Amano, S., Borsley, S., Leigh, D.A. et al. Chemical engines: driving systems away from equilibrium through catalyst reaction cycles. Nat. Nanotechnol. 16, 1057–1067 (2021). https://doi.org/10.1038/s41565-021-00975-4 ↵
- Lane N. (2018). Hot mitochondria?. PLoS biology, 16(1), e2005113. https://doi.org/10.1371/journal.pbio.2005113 ↵
relation between the amount of a material and the space it takes up, calculated as mass divided by volume.
SI unit of temperature