210. Sometimes the Helmholtz free energy F(T, V, N) divided by temperature, T, is an interestingquantity. For example, the quantity is proportional to the logarithm of the equilibrium constant orsolubilities.A. Derive a relationship showing thatFind the constant of proportionality.aFαυƏT TB. Suppose F(T) depends on temperature in the following way:F(T)=2aT²+bT.Find S(T) and U(T). C. For this and the next part of this problem, consider a transition between a helix anda coil state of a polymer. F/T is related is related to the ratio of populations aswhere KeqNhelixFT-In= = - In (Keq)Using F/T =2aT + b from above, at what temperature are the helixand coil in at equal populations?D. Assuming a > 0, does increasing the temperature favor the helix or the coil?

Answered: Image /qna-images/answer/73e41c11-432b-4212-8477-d2462686f126.jpg

Answered: 210. Sometimes the Helmholtz free…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter13: Temperature, Kinetic Theory, And The Gas Laws

Section: Chapter Questions

Problem 38PE: (a) In the deep space between galaxies, me density of atoms is as low as 106atoms/m3, and me...

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(a) In the deep space between galaxies, me density of atoms is as low as 106atoms/m3, and me temperature is a frigid 2.7 K. What is me pressure? (b) What volume (in m3) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?
(a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale.)
Lead has a density of 11.3 103 kg/m3 at 0C. (a) What is the density of lead at 90C? (b) Based on your answer to part (a), now consider a situation in which you plan to invest in a gold bar. Would you be better off buying it on a warm day? Explain.
The average life expectancy in Japan is 81 years. What is this time in SI units?
(a) Construct a table showing the macro states and all of the individual microstates for tossing 13 coins. (Use Table 15.5 as a guide.) (b) How many macro states are there? (c) What is the total number of microstates? (d) What percent chance is here of tossing 5 heads and 1 tail? (e) How much more likely are you to toss 3 heads and 3 tails than 5 heads and 1 tail? (Take me ratio of the number of microstates to find out.)
Unreasonable Results The temperature inside a supernova explosion is said to be 2.001013K. (a) What would the average velocity vrmsof hydrogen atoms be? (b) What is unreasonable about this velocity? (b) Which premise or assumption is responsible?
A triple-point cell such as the one shown in Figure 19.20 (page 571) is constructed and calibrated at sea level. It is then shipped to Denver, which is 1 mi above sea level. Can the researchers in the Denver lab use the triple-point cell just as in a laboratory at sea level, or will special adjustments be needed? Explain.
At 22.0C, the radius of a solid aluminum sphere is 7.00 cm. a. At what temperature will the volume of the sphere have increased by 3.00%? b. What is the increase in the spheres radius if it is heated to 250C? Assume = 22.2 106 K1 and = 66.6 106 K1.
Unreasonable results. (a) Find the temperature of 0.360 kg of water, modeled as an ideal gas, at a pressure of 1.01105 Pa if it has a volume of 0.615 m3. (b) What is unreasonable about this answer? How could you get a better answer?
In the text, it was shown that N/V=2.681025m3 for gas at STP. (a) Show that this quantity is equivalent to N/V=2.681019cm3, as stated. (b) About how many atoms are mere in one m3 (a cubic micrometer) at STP? (c) What does your answer to part (b) imply about the separation of Mama and molecules?
Five bicyclists are riding at the following speeds: 5.4 m/s, 5.7 m/s, 5.8 m/s, 6.0 m/s, and 6.5 m/s. (a) What is their average speed? (b) What is their rms speed?
One process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of about 14,0 mol/m3 and a temperature of about 60 . (a) Is CO2 a solid, liquid, gas, or supercritical fluid under those conditions? (b) The van der Waals constants for carbon dioxide are a=0.3658 Pa m6/mol2 and b=4.286105 m3/mol. Using the van der Waals equation, estimate pressure of CO2 at that temperature and density. `

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