Part g, h and i, please? One of the most important reactions in biology is photosynthesis. In this complex chemical process, plants combine molecules of carbon dioxide and waterto create glucose and oxygen. The reaction looks something like this:CO2 + H20 – C6H1206 + 02Of course the number of atoms don't balance on the two sides. You might be able to intuit your way to the correct counting (stoichiometry), but let's do it systematically by settingup equations.(a) Write the reaction asa CO2 + b H20 -→ c CGH1206 + d O2where a, b, c, and d are meant to be integers adjusted so that the number of each kind of atoms balance on each side. For this reaction, we have three kinds of atoms that must balance: carbon (C),hydrogen (H), and oxygen (0). Write three equations for a, b, c, and d that, if satisfied, will guarantee that the number of atoms of each kind are the same on each side of the reaction.(b) Find the smallest set of integers that will satisfy these equations. First, solve for a.(c) Solve for b. (c) Solve for b.(d) Solve for c.(e) Solve for d.(f) Write the correct stoichiometric equation for photosynthesis.(g) Dimensional analysisWhen we do dimensional analysis, we do something analogous to stoichiometry, but with multiplying instead of adding. Consider the diffusion constant that appears in Fick's first law:dnJ=-DdxIn this expression, J represents a flow of particles: number of particles per unit area per second, n represents a concentration of particles: number of particles per unit volume; and x represents adistance. We can assume that they have the following dimensionalities:• ) = 1/L?T• [n] = 1/L3• [x] = LFrom this, determine the dimensionality of D.(h) Einstein discovered a relation that expresses how D depends on the parameters of the system: the size of the particle diffusing (R), the viscosity of the fluid it is diffusing in(1),and the thermal energy parameter (kg7). These have the dimensionalities[kg 7] = ML2/T2[) = M/LT• [R] = LAssume that we can express Das a product of these three quantities to some power, like this:D= (kg7)a (b (R)Write eauations for a, b, and c that will guarantee that D will have the correct dimensionality for M, L, and T.(i) In this case, there were exactly the right number of parameters to give the same number of equations as there were unknowns. That will not always be the case, but sometimesthis method still can be made to work by adding physical knowledge about the dependences.Solve these equations and write an expression how D depends on the three parameters. (The correct equation has a factor of 1/(6n) that cannot be found from dimensional analysis. Make sure toinclude this factor in your answer.)

All quantities can be thought to be made out of fundamental quantities. We will use these ideas in…

Vhen we do dimensional analysis, we do something analogous to stoichiometry, but with multiplying instead of adding. Consider the diffusion constant that appears in Fick's first law: dn J=-D dx n this expression, J represents a flow of particles: number of particles per unit area per second, n represents a concentration of particles: number of particles per unit volume; and x represents a listance. We can assume that they have the following dimensionalities: • ) = 1/L2T • [n] = 1/L3 • [x] = L From this, determine the dimensionality of D. (h) Einstein discovered a relation that expresses how D depends on the parameters of the system: the size of the particle diffusing (R), the viscosity of the fluid it is diffusing in w,and the thermal energy parameter (kg 7). These have the dimensionalities • [kg 7] = ML2/T2 • ) = M/LT • [R] = L Assume that we can express Das a product of these three quantities to some power, like this: D= (kg na (b (R)C Vrite eauations for a, b, and c that will guarantee that D will have the correct dimensionality for M, L, and T. (i) In this case, there were exactly the right number of parameters to give the same number of equations as there were unknowns. That will not always be the case, but sometimes his method still can be made to work by adding physical knowledge about the dependences. Solve these equations and write an expression how D depends on the three parameters. (The correct equation has a factor of 1/(6n) that cannot be found from dimensional analysis. Make sure to nclude this factor in vour answer.)

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter10: Thermal Physics

Section: Chapter Questions

Problem 57AP