An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 1.7, Problem 68P
To determine
The time that the perfume needs to flow from one end of a room to the other end of the room.
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Let us consider a bacterial cell that depends on
chemical reactions using oxygen to produce energy.
The cell needs to obtain molecular oxygen from the
extra-cellular medium by diffusion through the cell
membrane.
We model the cell as a water-filled sphere of radius 1 µm. This means that we neglect the
presence of the internal structures of the cell: nucleus, nutrients, etc. The oxygen diffusion
coefficient (O2) in water at 25°C is 1.0x10-5 cm².s'.
Figure 1: Transmission electron microscope
Reminder: The distance travelled by diffusion can be picture of a bacterium. [from Wikipedia:
written as L(t) = V6Dt, where D is the diffusion
coefficient and t the diffusion time.
"Transmission Electron Microscopy"|
2. Diffusion as a function of time
People have measured the distance travelled by the oxygen molecule in water as a function of
time. The results are given in the table below.
0.1
t(s)
L (x10-“m)
log1o(t)
log10(L)
0.001
0.005
0.01
0.05
2.45
5.4
7.7
17.3
25.5
Draw the plot of L as a…
A very thin layer of oil floats on top of water. A drop of dye is placed at the center of the oil. The dye diffuses through the oil in all directions equally with a diffusion constant D0. Since the layer of oil is thin, we can assume the diffusion is two-dimensional. After a time T0 has passed, the dye has diffused a distance of 5 mm. If the dye had a diffusion constant of D0/3 what distance would the dye have diffused after a time T0/4? Give your answer in units of mm. (Round your answer to two decimal places.)
You are evaluating two biodegradable polymers, Polymer A and Polymer B, for material to release
hormonal birth control. The hormone drug is attached to the polymer backbone and drug is released
as the polymer degrades. You collect the following data on drug released from the polymer every 5
days over a 30-day study. State the mechanism by which Polymer A and Polymer B degrades and
calculate the rate constant, k, of degradation for Polymer A and Polymer B to 2 significant digits.
Show your work and upload your answers.
120%
70%
Polymer A
Polymer B
100%
60%
50%
80%
40%
60%
30%
40%
20%
20%
10%
0%
0%
0 5
10 15 20
25 30
0 5
10
15 20
25
30
Time (days)
Time (days)
Drug release
Drug release
Chapter 1 Solutions
An Introduction to Thermal Physics
Ch. 1.1 - Prob. 1PCh. 1.1 - The Rankine temperature scale (abbreviatedR) uses...Ch. 1.1 - Prob. 3PCh. 1.1 - Does it ever make sense to say that one object is...Ch. 1.1 - Prob. 5PCh. 1.1 - Give an example to illustrate why you cannot...Ch. 1.1 - Prob. 7PCh. 1.1 - For a solid, we also define the linear thermal...Ch. 1.2 - What is the volume of one mole of air, at room...Ch. 1.2 - Energy in Thermal Physics Estimate the number of...
Ch. 1.2 - Rooms A and B are the same size, and are connected...Ch. 1.2 - Calculate the average volume per molecule for an...Ch. 1.2 - A mole is approximately the number of protons in a...Ch. 1.2 - Calculate the mass of a mole of dry air, which is...Ch. 1.2 - Estimate the average temperature of the air inside...Ch. 1.2 - Prob. 16PCh. 1.2 - Prob. 17PCh. 1.2 - Prob. 18PCh. 1.2 - Suppose you have a gas containing hydrogen...Ch. 1.2 - Prob. 20PCh. 1.2 - During a hailstorm, hailstones with an average...Ch. 1.2 - Prob. 22PCh. 1.3 - Calculate the total thermal energy in a liter of...Ch. 1.3 - Calculate the total thermal energy in a gram of...Ch. 1.3 - List all the degrees of freedom, or as many as you...Ch. 1.4 - A battery is connected in series to a resistor,...Ch. 1.4 - Give an example of a process in which no heat is...Ch. 1.4 - Estimate how long it should take to bring a cup of...Ch. 1.4 - A cup containing 200 g of water is sitting on your...Ch. 1.4 - Put a few spoonfuls of water into a bottle with a...Ch. 1.5 - Imagine some helium in cylinder with an initial...Ch. 1.5 - Prob. 32PCh. 1.5 - An ideal gas is made to undergo the cyclic process...Ch. 1.5 - An ideal diatomic gas, in a cylinder with a...Ch. 1.5 - Prob. 35PCh. 1.5 - In the course of pumping up a bicycle tire, a...Ch. 1.5 - Prob. 37PCh. 1.5 - Two identical bubbles of gas form at the bottom of...Ch. 1.5 - By applying Newtons laws to the oscillations of a...Ch. 1.5 - In problem 1.16 you calculated the pressure of...Ch. 1.6 - To measure the heat capacity of an object, all you...Ch. 1.6 - The specific heat capacity of Albertsons Rotini...Ch. 1.6 - Calculate the heat capacity of liquid water per...Ch. 1.6 - Prob. 44PCh. 1.6 - Prob. 45PCh. 1.6 - Measured heat capacities of solids and liquids are...Ch. 1.6 - Your 200-g cup of tea is boiling-hot. About how...Ch. 1.6 - When spring finally arrives in the mountains, the...Ch. 1.6 - Prob. 49PCh. 1.6 - Consider the combustion of one mole of methane...Ch. 1.6 - Use the data at the back of this book to determine...Ch. 1.6 - The enthalpy of combustion of a gallon (3.8...Ch. 1.6 - Look up the enthalpy of formation of atomic...Ch. 1.6 - Prob. 54PCh. 1.6 - Heat capacities are normally positive, but there...Ch. 1.7 - Calculate the rate of heat conduction through a...Ch. 1.7 - Home owners and builders discuss thermal...Ch. 1.7 - According to a standard reference table, the R...Ch. 1.7 - Make a rough estimate of the total rate or...Ch. 1.7 - A frying pan is quickly heated on the stovetop to...Ch. 1.7 - Geologists measure conductive heat flow out of the...Ch. 1.7 - Consider a uniform rod of material whose...Ch. 1.7 - Prob. 63PCh. 1.7 - Make a rough estimate of the thermal conductivity...Ch. 1.7 - Prob. 65PCh. 1.7 - In analogy with the thermal conductivity, derive...Ch. 1.7 - Make a rough estimate of how far food coloring (or...Ch. 1.7 - Prob. 68PCh. 1.7 - Imagine a narrow pipe, filled with fluid, in which...Ch. 1.7 - Prob. 70P
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- A patient uses an oxygen tank to breathe. At the beginning of your shift, the gauge on the tank shows the internal gas pressure to be 250 psi. At the end of your shift you check the tank again and find the pressure to be 25 psi (psi stands for pounds per square inch; it is another unit of pressure). The number of molecules is directly proportional to the pressure of the system. What proportion of the gas molecules was used?arrow_forwardYou may have noticed that latex helium balloons tend to shrink rather quickly; a balloon filled with air lasts a lot longer. Balloons shrink because gas diffuses out of them. The rate of diffusion is faster for smaller particles and for particles of higher speed. Diffusion is also faster when there is a large difference in concentration between two sides of a membrane. Given these facts, explain why an air-filled balloon lasts longer than a helium balloon.arrow_forwardImagine you are in line to enter a brand new shopping mall and you are very much excited because after months of waiting, you will now be able to enter shopping malls after the pandemic. The stores comprising the mall are very popular. These stores include Converse, Gucci, Jansport, Fendi and all other popular brands, and so the demand to enter is very high. Security guards only allow one person through the doors at a time. As a result, the line and the wait are quite long. To add to the chaos, the waiting crowd is made mostly of frequent shoppers who are growing very impatient and holding up the line with their constant complains. Together, these factors affect the flow of customers into the shopping mall, just as electric resistance affects the flow of charges through a current. 1. What makes less resistance favorable in a circuit? 2.If the guard formed two adjacent lines to allow two people into the mall at a time, we would expect the mall to be filled up faster. If we encased these…arrow_forward
- For a substance with a diffusion coefficient (D) of 1 x 10E-5 cm2.s-1, what is the diffusion time along a path of 1 micrometer (um), a distance that is roughly the length of a bacterial cell? (Remember that x2 = 2Dt.) A. 5 ms B. 50 ms C. 0.5 ms D. 500 ms O E. 500 sarrow_forwardThe oxygen consumption at rest for a 70-kg person is 14.5 liter/h and that 2% of this requirement is provided by the diffusion of oxygen through the skin. Assuming that the skin surface area of the person is 1.7m2 , calculate the diffusion rate for oxygen through the skin in liter/h-cm2.arrow_forwardA water molecule has a diameter of about 0.275 nm. How many hours would it take for a water molecule to diffuse across the surface of a Starbucks Venti sized cup of coffee whose diameter is 3.8 inches? Assume that coffee is liquid H20 for your calculation. The diffusion coefficient of H2O in water is 2.26 X 109 m2sarrow_forward
- (a) Suppose that a person has an average heart rate of 72.0 beats/mm. How many beats does he or she have in 2.0 years? (b) In 2.00 years? (c) In 2.000 years?arrow_forward(a) What is the order of magnitude of the number of micro organisms in the human intestinal tract? A typical bacterial length scale is 106 m. Estimate the intestinal volume and assume 1% of it is occupied by bacteria. (b) Does the number of bacteria suggest whether the bacteria are beneficial, dangerous, or neutral for the human body? What functions could they serve?arrow_forwardMany entertainers have facial tattoos. Assuming the ink is in the extracellular space, how long would it take to diffuse (or blur) 10mm? Assume the diffusion coefficient of the ink is 2.5*10-8 cm2/s and that 2 dimensional diffusion occurs in the skin. (hint: use similar units for the variables) 29 days 116 days 231 days 58 daysarrow_forward
- Why does pressure have a direct relationship with absolute temperature? Kindly explain this law in terms of microscopic behavior of particles. Volume versus the reciprocal of pressure How well does the graph of volume versus the reciprocal of the pressure support the idea that volume of a gas at constant temperature is inversely proportional to the pressure of the gas? Why does pressure have an inverse relationship with volume? Kindly explain this law in terms of microscopic behavior of particles.arrow_forwardThe small capillaries in the lungs are in close contact with the alveoli. A red blood cell takes up oxygen during the 0.5 s that it squeezes through a capillary at the surface of an alveolus. What is the diffusion time for oxygen across the 1-μm -thick membrane separating air from blood? Assume that the diffusion coefficient for oxygen in tissue is 2×10^−11 m2/s. Give your answer to 1 significant figure.arrow_forwardThe total lung capacity of a typical adult is 4.6 L. Approximately 20% of the air is oxygen. ▾ Part A At sea level and at a body temperature of 37° C, how many oxygen molecules do the lungs contain at the end of a strong inhalation? ► View Available Hint(s) ΕΠΙ ΑΣΦ N= Submit h ? molecules of oxygenarrow_forward
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