To calculate the standard molar entropy, s m, set p p in the expression for sm. Lecture 8 entropy of the ideal gas, entropy of mixing and gibbs paradox, indistinguishable particles, sackurtetrode equation lecture 9 canonical ensemble, energy fluctuations and specific heat, equivalence of microcanonical and canonical ensembles. The entropy is then writing the expression above for q as bt 32 gives using this and stirlings approximation in the expression for the entropy gives. Derivation of sackurtetrode equation physics forums. The sackurtetrode equation tells us how to compute the entropy of a monatomic ideal gas think helium or any other noble gases. Download pdf insecurity and emerging biotechnology book full free. An equation for the translational entropy of an ideal gas made up of free fermions explanation of sackurtetrode equation. On the sackurtetrode equation in an expanding universe. I have seen it in the derivation of the boltzmann distribution.
Derivation of the sackurtetrode equation brainmass. Revised and extended version, main results unchange. Derivation of the sackur tetrode equation add remove this content was copied from view the original, and get the alreadycompleted solution here. The grand achievement in the derivation of this equation was the discretization of phase space for massive particles, expressed as. Statistical mechanics what you need to know ptcl, oxford. These give a more detailed description of its regime of validity. Can you derive sackurtetrode equation entropy for ideal. My thermodynamics text does not go through the whole derivation, but that is how it says to derive it. Of course this is absurd, so the sackurtetrode equation must be invalid at very low temperatures.
According to the sackurtetrode equation, the entropy. The sackurtetrode equation to calculate the entropy of a monoatomic ideal gas is, here, n is the number of molecules, k is the boltzmann constant, v is the volume, m is the atomic mass, u is the internal energy, and h is the planks constant. First of all, note that if the energy and number of molecules remains xed, an increase in volume, vi. Expert answer 100% 4 ratings previous question next question. Me346a introduction to statistical mechanics wei cai stanford university win 2011 handout 6. Clausius versus sackurtetrode entropies philsciarchive. This equation has been developed independently by hugo tetrode and otto sackur 4. According to the sackurtetrode equation, the entropy of. On the sackurtetrode equation in an expanding universe where a atis the scale factor of the evolution, or roughly speaking, the universe radius, so that v a3 varies with the universe expansion. The sackur tetrode equation is an expression for the entropy of a monatomic classical ideal gas which incorporates quantum considerations. You can derive the sackurtetrode equation by solving for the entropy of an ideal gas using stirlings approximation applied to the multiplicity formula. These results can be cast into forms which are easier to remember.
To find the chemical potential, we can use another standard relation. According to the sackurtetrode equation, the entropy of a monatomic ideal gas can become negative when its temperature and hence its energy is sufficiently low. Why is the entropy greater than that of a mole of helium under the same conditions. Then he considers a system with n degrees of freedom and phase space. Oct 14, 2011 you can derive the sackur tetrode equation by solving for the entropy of an ideal gas using stirlings approximation applied to the multiplicity formula.
Unlike the ideal gas, for which there are three independent variables, n, t, and v, the photon gas has just two independent, controllable variables, t and v. According to the sackurtetrode equation, the entropy of a. The fact that quantum mechanics makes particles eveninprinciple indistinguishable is huge, and it resolves the gibbs paradox, leading to the sackur tetrode equation. In particular the sackur tetrode equation for the entropy of the ideal gas is also valid in the case of an expanding universe, provided that the constant value that represents the current entropy of the universe is appropriately chosen. But i dont know the physical significance of it here. Sackurtetrode equation article about sackurtetrode. On the legendre transformation and the sackurtetrode equation. Derive the sackurtetrode equation physics stack exchange. Thermodynamics january 26, 2011 contents 1 laws of thermodynamics 2.
The sackurtetrode equation is named for hugo martin tetrode1 18951931 and otto sackur2 18801914, who developed it. Macrostate and microstate, phase space, elementary concept of ensemble, entropy and thermodynamic probability, maxwellboltzmann distribution law, partition function, thermodynamic functions of an ideal gas, classical entropy expression, gibbs paradox, sackur. By plugging the variables in and solving, it comes very close to the st equation. By similar reasoning, he limited the spacing of the allowed states for the elements, energytime. I posted the following solution on this board wanting to get opinions of the validity of a solution using only the microcanonical ensemble. On the 100th anniversary of the sackurtetrode equation. The information constraints youre looking for over the probability distribution of variables are. Derive the formula for the entropy of an ideal monoatomic gas using the microcanonical ensemble. The actual significance of this equation is negligible and can be calculated by multiplying the equation with. Legendre transformations iii, the sackurtetrode equation. Lecture 8 entropy of the ideal gas, entropy of mixing and gibbs paradox, indistinguishable particles, sackur tetrode equation lecture 9 canonical ensemble, energy fluctuations and specific heat, equivalence of microcanonical and canonical ensembles.
An alternative expression to the sackurtetrode entropy. Insecurity and emerging biotechnology available for download and read online in other formats. The structure of the sackur tetrode equation is illuminating to students and is worth introducing. Please be warned that these are the notes i prepare for myself to lecture from they are not in general carefully prepared for others to read. Feb 24, 2010 on the sackurtetrode equation in an expanding universe. Even if one were willing to say that e is a function of t through s, i.
Onthe100thanniversaryofthe sackurtetrodeequation arxiv. The structure of the sackurtetrode equation is illuminating to students and is worth introducing. Download hires image download to mspowerpoint cite this. The principal message of this book is that thermodynamics and statistical mechanics will benefit from replacing the unfortunate, misleading and mysterious term entropy with a more familiar, meaningful and appropriate term such as information, mi. The sackur tetrode equation gives us some insight into this problem. Sackurtetrode equation unionpedia, the concept map. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. For example, suppose the ideal gas is in a pistoncylinder apparatus such as we discussed. Oct 18, 2019 the sackurtetrode equation is named for hugo martin tetrode1 18951931 and otto sackur2 18801914, who developed it independently as a solution of boltzmanns gas statistics and entropy equations, at about the same time in 1912. Sackurtetrode equation article about sackurtetrode equation by the free dictionary. This pioneering investigation about 100 years ago incorporates quantum considerations. In particular the sackurtetrode equation for the entropy of the ideal gas is also valid in the case of an expanding universe, provided that the constant value that represents the current entropy of the universe is appropriately chosen. The sackurtetrode equation is an expression for the entropy of a monatomic classical ideal gas which incorporates quantum considerations which give a more detailed description of its regime of validity.
The entropy of a monatomic ideal gas is given by the sackurtetrode equation which can be written in the form. Lets check this out with the sackur tetrode formula for an ideal gas. Pdf on the sackurtetrode equation in an expanding universe. This, together with boltzmanns equation, gave them an expression for the absolute entropy, the sackurtetrode equation. Pdf insecurity and emerging biotechnology download full. The sackurtetrode equation and the measure of entropy. Sackurtetrode equation 3 u 3 2 nkt 3 2 nrt3739 j 15 the mass of a mole of argon is 39. Robbing a student of this fact, and the amount of brainwarp that it creates, is not a bad thing necessarily, but its also not necessarily a good thing. The sackurtetrode equation is an expression for the entropy of a monatomic classical ideal gas which incorporates quantum considerations. These metrics are regularly updated to reflect usage leading up to the last few days.
The topics covered include the fundamentals of probability and information theory. Sackur adhered more to the style of max plancks school of thermodynamics. On the sackurtetrode equation in an expanding universe core. Method to calculate the molar entropy, sm, from eqn 16. An equation for the translational entropy of an ideal gas made up of free fermions explanation of sackur tetrode equation. Thermodynamic origin of kappa distributions iopscience. An expression for the entropy of a monoatomic classical ideal gas is known as the sackurtetrode equation. Use the sackur tetrode equation to calculate the entropy of a mole of argon gas at room temperature and atmospheric pressure. Usage of partition function in derivation of sackurtetrode. Fundamentals of electromagnetics maw miah 1982 tata.
This content was copied from view the original, and get the alreadycompleted solution here. Fundamentals of electromagnetics maw miah 1982 tata mcgraw. Sackurtetrode equation free expansion no heat, no work, but entropy increases. Hugo tetrode and otto sackur independently developed an equation for the entropy using a solution of the boltzmann statistic. Mar 26, 2018 an expression for the entropy of a monoatomic classical ideal gas is known as the sackur tetrode equation. The sackurtetrode equation gives us some insight into this problem. Ppt ideal gas in microcanonical ensemble powerpoint. The sackur tetrode equation is an expression for the entropy of a monatomic classical ideal gas which incorporates quantum considerations which give a more detailed description of its regime of validity. The sackurtetrode equation and the measure of entropy francisco jos e panos exp osito volves vapor pressure measurements as well as calorimetric ones 1, 2, whereas the other is purely calorimetric 3.
In these statistical mechanics notes pdf, you will study the derivation of the macroscopic parameters internal energy, pressure, specific heat etc. Dec 25, 20 the sackurtetrode equation tells us how to compute the entropy of a monatomic ideal gas think helium or any other noble gases. H pereira 1 worked with the sackur tetrode equation in an expanding universe. Me346a introduction to statistical mechanics wei cai. The sackur tetrode equation and the measure of entropy francisco jos e panos exp osito volves vapor pressure measurements as well as calorimetric ones 1, 2, whereas the other is purely calorimetric 3. The fact that quantum mechanics makes particles eveninprinciple indistinguishable is huge, and it resolves the gibbs paradox, leading to the sackurtetrode equation. The idea is to measure the increment of entropy a sub. Zeroth law \transitivity of thermodynamic equilibrium if systems a and b are in thermal equilibrium. My hand written class lecture notes are being scanned and uploaded for you to view. What is the significance of the sackurtetrode equation.
We have analyzed the latter, since the vapor pressure method relies on this one. Temperature is a state quantity which is unknown in classical mechanics. W e can envisage building a photon gas from ener gy stored in the container walls. The purpose of this paper is to provide an alternative expression for the entropy in terms of the heisenberg uncertainty relation. Sackur tetrode equation 3 u 3 2 nkt 3 2 nrt3739 j 15 the mass of a mole of argon is 39. The thomas group ptcl, oxford the thomaspenfold group. Download product flyer is to download pdf in new tab. Macrostate and microstate, phase space, elementary concept of ensemble, entropy and thermodynamic probability, maxwellboltzmann distribution law, partition function, thermodynamic functions of an ideal gas, classical entropy expression, gibbs paradox, sackur tetrode equation. Can someone please explain the process of how you derive the sackurtetrode equation from this.
130 1237 1127 1511 1301 1127 1499 1246 994 359 966 1365 754 1497 927 179 156 1611 607 1577 145 969 1284 1243 1230 60 564 1453 1269 387 1198 189 838 605 726 302 217 1213 338 1238