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In [[quantum mechanics]], the results of the quantum [[particle in a box]] can be used to look at the equilibrium situation for a quantum ideal '''gas in a box''' which is a box containing a large number of molecules which do not interact with each other except for instantaneous thermalizing collisions. This simple model can be used to describe the classical [[ideal gas]] as well as the various quantum ideal gases such as the ideal massive [[Fermi gas]], the ideal massive [[Bose gas]] as well as [[black body]] radiation which may be treated as a massless Bose gas, in which thermalization is usually assumed to be facilitated by the interaction of the photons with an equilibrated mass. | |||
Using the results from either [[Maxwell-Boltzmann statistics]], [[Bose-Einstein statistics]] or [[Fermi-Dirac statistics]], and considering the limit of a very large box, the [[Thomas-Fermi approximation]] is used to express the degeneracy of the energy states as a differential, and summations over states as integrals. This enables thermodynamic properties of the gas to be calculated with the use of the [[partition function (statistical mechanics)|partition function]] or the [[grand partition function]]. These results will be applied to both massive and massless particles. More complete calculations will be left to separate articles, but some simple examples will be given in this article. | |||
==Thomas–Fermi approximation for the degeneracy of states== | |||
{{Main|Thomas–Fermi model}} | |||
For both massive and massless [[particles in a box]], the states of a particle are | |||
enumerated by a set of quantum numbers | |||
[''n''<sub>''x''</sub>, ''n''<sub>''y''</sub>, ''n''<sub>''z''</sub>]. The magnitude of the momentum is given by | |||
:<math>p=\frac{h}{2L}\sqrt{n_x^2+n_y^2+n_z^2} \qquad \qquad n_x,n_y,n_z=1,2,3,\ldots </math> | |||
where ''h '' is [[Planck's constant]] and ''L '' is the length of a side of the box. | |||
Each possible state of a particle can be thought of as a point on a 3-dimensional | |||
grid of positive integers. The distance from the origin to any point will be | |||
:<math>n=\sqrt{n_x^2+n_y^2+n_z^2}=\frac{2Lp}{h}</math> | |||
Suppose each set of quantum numbers specify ''f '' states where ''f '' is | |||
the number of internal degrees of freedom of the particle that can be altered by | |||
collision. For example, a spin 1/2 particle would have ''f=2'', one for each spin | |||
state. For large values of ''n '', the number of states with magnitude of momentum less than or equal to ''p '' from the above | |||
equation is approximately | |||
:<math> | |||
g=\left(\frac{f}{8}\right) \frac{4}{3}\pi n^3 | |||
= \frac{4\pi f}{3} \left(\frac{Lp}{h}\right)^3 | |||
</math> | |||
which is just ''f '' times the volume of a sphere of radius ''n '' divided by eight | |||
since only the octant with positive ''n<sub>i </sub>'' is considered. Using a continuum approximation, the number of | |||
states with magnitude of momentum between ''p '' and ''p+dp '' is | |||
therefore | |||
:<math> | |||
dg=\frac{\pi}{2}~f n^2\,dn = \frac{4\pi fV}{h^3}~ p^2\,dp | |||
</math> | |||
where ''V=L<sup>3</sup> '' is the volume of the box. Notice that in using this | |||
continuum approximation, the ability to characterize the low-energy | |||
states is lost, including the ground state where ''n<sub>i </sub>=1''. For most cases this | |||
will not be a problem, but when considering Bose-Einstein condensation, in which a | |||
large portion of the gas is in or near the ground state, the | |||
ability to deal with low energy states becomes important. | |||
Without using the continuum approximation, the number of particles with | |||
energy ε<sub>i </sub> is given by | |||
:<math> | |||
N_i = \frac{g_i}{\Phi(\epsilon_i)} | |||
</math> | |||
where | |||
:{| | |||
|- | |||
|<math>\! g_i</math>, [[Degenerate energy level|degeneracy]] of state ''i'' | |||
|- | |||
| | |||
|- | |||
|<math>\Phi(\epsilon_i) = | |||
\begin{cases} | |||
e^{\beta(\epsilon_i-\mu)}, & \mbox{for particles obeying Maxwell-Boltzmann statistics } \\ | |||
e^{\beta(\epsilon_i-\mu)}-1, & \mbox{for particles obeying Bose-Einstein statistics}\\ | |||
e^{\beta(\epsilon_i-\mu)}+1, & \mbox{for particles obeying Fermi-Dirac statistics}\\ | |||
\end{cases}</math> | |||
|- | |||
|with β = ''1/kT '', [[Boltzmann's constant]] ''k'', [[temperature]] ''T'', and [[chemical potential]] ''μ'' . | |||
|- | |||
|(See [[Maxwell-Boltzmann statistics]], [[Bose-Einstein statistics]], and [[Fermi-Dirac statistics]].) | |||
|} | |||
Using the continuum approximation, the number of particles ''dN<sub>E</sub>'' with energy between | |||
''E'' and ''E+dE'' is: | |||
:<math>dN_E= \frac{dg_E}{\Phi(E)} </math> | |||
:where <math>\!dg_E</math> is the number of states with energy between ''E'' and ''E+dE'' . | |||
==Energy distribution== | |||
Using the results derived from the previous sections of this article, some distributions for the "gas in a box" can now be determined. For a system of particles, the distribution <math>P_A</math> for a variable <math>A</math> is defined through the expression <math>P_AdA</math> which is the fraction of particles that have values for <math>A</math> between <math>A</math> and <math>A+dA</math> | |||
:<math>P_A~dA = \frac{dN_A}{N} = \frac{dg_A}{N\Phi_A}</math> | |||
where | |||
:<math>dN_A</math> , number of particles which have values for <math>A</math> between <math>A</math> and <math>A+dA</math> | |||
:<math>dg_A</math> , number of states which have values for <math>A</math> between <math>A</math> and <math>A+dA</math> | |||
:<math>\Phi_A^{-1}</math> , probability that a state which has the value <math>A</math> is occupied by a particle | |||
: <math>N</math> , total number of particles. | |||
It follows that: | |||
:<math>\int_A P_A~dA = 1</math> | |||
For a momentum distribution <math>P_p</math>, the fraction of particles with magnitude of momentum between <math>p</math> and <math>p+dp</math> is: | |||
:<math>P_p~dp = \frac{Vf}{N}~\frac{4\pi}{h^3\Phi_p}~p^2dp</math> | |||
and for an energy distribution <math>P_E</math>, the fraction of particles with energy between <math>E</math> and <math>E+dE</math> is: | |||
:<math> | |||
P_E~dE = P_p\frac{dp}{dE}~dE | |||
</math> | |||
For a particle in a box (and for a free particle as well), the relationship between energy <math>E</math> and momentum <math>p</math> is different for massive and massless particles. For massive particles, | |||
:<math> E=\frac{p^2}{2m}</math> | |||
while for massless particles, | |||
:<math>E=pc\,</math> | |||
where <math>m</math> is the mass of the particle and <math>c</math> is the speed of light. | |||
Using these relationships, | |||
* For massive particles | |||
:<math>\begin{alignat}{2} | |||
dg_E & = \quad \ \left(\frac{Vf}{\Lambda^3}\right) | |||
\frac{2}{\sqrt{\pi}}~\beta^{3/2}E^{1/2}~dE \\ | |||
P_E~dE & = \frac{1}{N}\left(\frac{Vf}{\Lambda^3}\right) | |||
\frac{2}{\sqrt{\pi}}~\frac{\beta^{3/2}E^{1/2}}{\Phi(E)}~dE \\ | |||
\end{alignat} | |||
</math> | |||
where Λ is the [[thermal wavelength]] of the gas. | |||
:<math> | |||
\Lambda =\sqrt{\frac{h^2 \beta }{2\pi m}} | |||
</math> | |||
This is an important quantity, since when Λ is on the order of the | |||
inter-particle distance <math>(V/N)</math><sup>''1/3''</sup>, quantum effects begin to | |||
dominate and the gas can no longer be considered to be a Maxwell-Boltzmann gas. | |||
* For massless particles | |||
:<math>\begin{alignat}{2} | |||
dg_E & = \quad \ \left(\frac{Vf}{\Lambda^3}\right) | |||
\frac{1}{2}~\beta^3E^2~dE \\ | |||
P_E~dE & = \frac{1}{N}\left(\frac{Vf}{\Lambda^3}\right) | |||
\frac{1}{2}~\frac{\beta^3E^2}{\Phi(E)}~dE \\ | |||
\end{alignat} | |||
</math> | |||
where Λ is now the [[thermal wavelength]] for massless particles. | |||
:<math>\Lambda = \frac{ch\beta}{2\,\pi^{1/3}}</math> | |||
==Specific examples== | |||
The following sections give an example of results for some specific cases. | |||
===Massive Maxwell-Boltzmann particles=== | |||
For this case: | |||
:<math>\Phi(E)=e^{\beta(E-\mu)}</math> | |||
Integrating the energy distribution function and solving for ''N'' gives | |||
:<math>N = \left(\frac{Vf}{\Lambda^3}\right)\,\,e^{\beta\mu}</math> | |||
Substituting into the original energy distribution function gives | |||
:<math>P_E~dE = 2 \sqrt{\frac{\beta^3 E}{\pi}}~e^{-\beta E}~dE</math> | |||
which are the same results obtained classically for the | |||
[[Maxwell-Boltzmann distribution]]. Further results can be found in the classical section of the article on the [[ideal gas]]. | |||
===Massive Bose-Einstein particles=== | |||
For this case: | |||
:<math>\Phi(E)=\frac{e^{\beta E}}{z}-1\,</math> | |||
:where <math> z=e^{\beta\mu}.\,</math> | |||
Integrating the energy distribution function and solving for ''N'' gives | |||
the [[particle number]] | |||
:<math>N = \left(\frac{Vf}{\Lambda^3}\right)\textrm{Li}_{3/2}(z)</math> | |||
where Li<sub>s</sub>(z) is the [[polylogarithm]] function and Λ is the | |||
[[thermal wavelength]]. The polylogarithm term must always be positive | |||
and real, which means its value will go from 0 to ζ(3/2) as ''z '' goes from | |||
0 to 1. As the temperature drops towards zero, Λ will become larger and larger, | |||
until finally Λ will reach a critical value Λ<sub>c </sub> where ''z=1'' and | |||
:<math>N = \left(\frac{Vf}{\Lambda_c^3}\right)\zeta(3/2).</math> | |||
The temperature at which Λ=Λ<sub>c</sub> is the critical temperature. For | |||
temperatures below this critical temperature, the above equation for the particle number | |||
has no solution. The critical temperature is the temperature at which a Bose-Einstein | |||
condensate begins to form. The problem is, as mentioned | |||
above, that the ground state has been ignored in the continuum approximation. It turns | |||
out, however, that the above equation for particle number expresses the number of bosons in excited states | |||
rather well, and thus: | |||
:<math> | |||
N=\frac{g_0 | |||
z}{1-z}+\left(\frac{Vf}{\Lambda^3}\right)\textrm{Li}_{3/2}(z) | |||
</math> | |||
where the added term is the number of particles in the ground state. (The ground | |||
state energy has been ignored.) This equation will hold down to zero temperature. | |||
Further results can be found in the article on the ideal [[Bose gas]]. | |||
===Massless Bose-Einstein particles (e.g. black body radiation)=== | |||
For the case of massless particles, the massless energy distribution function must be used. It is convenient to convert this function to a frequency distribution function: | |||
:<math> | |||
P_\nu~d\nu = \frac{h^3}{N}\left(\frac{Vf}{\Lambda^3}\right) | |||
\frac{1}{2}~\frac{\beta^3\nu^2}{e^{(h\nu-\mu)/kT}-1}~d\nu | |||
</math> | |||
where Λ is the thermal wavelength for massless particles. The spectral energy density (energy per unit volume per unit frequency) is then | |||
:<math>U_\nu~d\nu = \left(\frac{N\,h\nu}{V}\right) P_\nu~d\nu = \frac{4\pi f h\nu^3 }{c^3}~\frac{1}{e^{(h\nu-\mu)/kT}-1}~d\nu.</math> | |||
Other thermodynamic parameters may be derived analogously to the case for massive particles. For example, integrating the frequency distribution function and solving for ''N'' gives the number of particles: | |||
:<math>N=\frac{16\,\pi V}{c^3h^3\beta^3}\,\mathrm{Li}_3\left(e^{\mu/kT}\right).</math> | |||
The most common massless Bose gas is a [[photon gas]] in a [[black body]]. Taking the "box" to be a black body cavity, the photons are continually being absorbed and re-emitted by the walls. When this is the case, the number of photons is not conserved. In the derivation of [[Bose-Einstein statistics]], when the restraint on the number of particles is removed, this is effectively the same as setting the chemical potential (''μ'') to zero. Furthermore, since photons have two spin states, the value of ''f'' is 2. The spectral energy density is then | |||
:<math>U_\nu~d\nu = \frac{8\pi h\nu^3 }{c^3}~\frac{1}{e^{h\nu/kT}-1}~d\nu </math> | |||
which is just the spectral energy density for [[Planck's law of black body radiation]]. Note that the [[Wien approximation|Wien distribution]] is recovered if this procedure is carried out for massless Maxwell-Boltzmann particles, which approximates a Planck's distribution for high temperatures or low densities. | |||
In certain situations, the reactions involving photons will result in the conservation of the number of photons (e.g. [[light-emitting diode]]s, "white" cavities). In these cases, the photon distribution function will involve a non-zero chemical potential. (Hermann 2005) | |||
Another massless Bose gas is given by the [[Debye model]] for heat capacity. This considers a gas of [[phonons]] in a box and differs from the development for photons in that the speed of the phonons is less than light speed, and there is a maximum allowed wavelength for each axis of the box. This means that the integration over phase space cannot be carried out to infinity, and instead of results being expressed in [[polylogarithm]]s, they are expressed in the related [[Debye function]]s. | |||
===Massive Fermi-Dirac particles (e.g. electrons in a metal)=== | |||
For this case: | |||
:<math>\Phi(E)=e^{\beta(E-\mu)}+1.\,</math> | |||
Integrating the energy distribution function gives | |||
:<math>N=\left(\frac{Vf}{\Lambda^3}\right)\left[-\textrm{Li}_{3/2}(-z)\right]</math> | |||
where again, Li<sub>s</sub>(z) is the [[polylogarithm]] function and Λ is the | |||
[[thermal de Broglie wavelength]]. Further results can be found in the article on the | |||
ideal [[Fermi gas]]. | |||
== References == | |||
* {{cite journal| last = Herrmann| first = F.| coauthors = Würfel, P. | |||
|date=August 2005 | |||
| title = Light with nonzero chemical potential| journal = American Journal of Physics | |||
| volume = 73| issue = 8| pages = 717–723| doi = 10.1119/1.1904623 | |||
| url = http://scitation.aip.org/journals/doc/AJPIAS-ft/vol_73/iss_8/717_1.html | |||
| accessdate = 2006-11-20|bibcode = 2005AmJPh..73..717H }} | |||
* {{cite book |last=Huang |first=Kerson |authorlink= | |||
|title=Statistical Mechanics |year=1967 |publisher=John Wiley & Sons |location=New York}} | |||
* {{cite book |last=Isihara |first=A. | |||
|title=Statistical Physics |year=1971 |publisher=Academic Press |location=New York}} | |||
* {{cite book |last=Landau |first=L. D.|coauthors=E. M. Lifshitz | |||
|title=Statistical Physics |edition=3rd Edition Part 1 |year=1996 | |||
|publisher=Butterworth-Heinemann |location=Oxford}} | |||
* {{cite journal| last = Yan| first = Zijun| year = 2000 | |||
| title = General thermal wavelength and its applications| journal = Eur. J. Phys. | |||
| volume = 21| pages = 625–631|doi=10.1088/0143-0807/21/6/314 | |||
| url = http://www.iop.org/EJ/article/0143-0807/21/6/314/ej0614.pdf | |||
| format = PDF| accessdate = 2006-11-20|bibcode = 2000EJPh...21..625Y| issue = 6 }} | |||
* {{cite web |url=http://clesm.mae.ufl.edu/wiki.pub/index.php/Configuration_integral_(statistical_mechanics) |title=Configuration_integral_(statistical_mechanics) |accessdate=2008-10-12 |last=Vu-Quoc |first=Loc }} | |||
[[Category:Statistical mechanics]] |
Revision as of 16:16, 3 December 2013
In quantum mechanics, the results of the quantum particle in a box can be used to look at the equilibrium situation for a quantum ideal gas in a box which is a box containing a large number of molecules which do not interact with each other except for instantaneous thermalizing collisions. This simple model can be used to describe the classical ideal gas as well as the various quantum ideal gases such as the ideal massive Fermi gas, the ideal massive Bose gas as well as black body radiation which may be treated as a massless Bose gas, in which thermalization is usually assumed to be facilitated by the interaction of the photons with an equilibrated mass.
Using the results from either Maxwell-Boltzmann statistics, Bose-Einstein statistics or Fermi-Dirac statistics, and considering the limit of a very large box, the Thomas-Fermi approximation is used to express the degeneracy of the energy states as a differential, and summations over states as integrals. This enables thermodynamic properties of the gas to be calculated with the use of the partition function or the grand partition function. These results will be applied to both massive and massless particles. More complete calculations will be left to separate articles, but some simple examples will be given in this article.
Thomas–Fermi approximation for the degeneracy of states
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For both massive and massless particles in a box, the states of a particle are enumerated by a set of quantum numbers [nx, ny, nz]. The magnitude of the momentum is given by
where h is Planck's constant and L is the length of a side of the box. Each possible state of a particle can be thought of as a point on a 3-dimensional grid of positive integers. The distance from the origin to any point will be
Suppose each set of quantum numbers specify f states where f is the number of internal degrees of freedom of the particle that can be altered by collision. For example, a spin 1/2 particle would have f=2, one for each spin state. For large values of n , the number of states with magnitude of momentum less than or equal to p from the above equation is approximately
which is just f times the volume of a sphere of radius n divided by eight since only the octant with positive ni is considered. Using a continuum approximation, the number of states with magnitude of momentum between p and p+dp is therefore
where V=L3 is the volume of the box. Notice that in using this continuum approximation, the ability to characterize the low-energy states is lost, including the ground state where ni =1. For most cases this will not be a problem, but when considering Bose-Einstein condensation, in which a large portion of the gas is in or near the ground state, the ability to deal with low energy states becomes important.
Without using the continuum approximation, the number of particles with energy εi is given by
where
, degeneracy of state i with β = 1/kT , Boltzmann's constant k, temperature T, and chemical potential μ . (See Maxwell-Boltzmann statistics, Bose-Einstein statistics, and Fermi-Dirac statistics.)
Using the continuum approximation, the number of particles dNE with energy between E and E+dE is:
Energy distribution
Using the results derived from the previous sections of this article, some distributions for the "gas in a box" can now be determined. For a system of particles, the distribution for a variable is defined through the expression which is the fraction of particles that have values for between and
where
- , number of particles which have values for between and
- , number of states which have values for between and
- , probability that a state which has the value is occupied by a particle
- , total number of particles.
It follows that:
For a momentum distribution , the fraction of particles with magnitude of momentum between and is:
and for an energy distribution , the fraction of particles with energy between and is:
For a particle in a box (and for a free particle as well), the relationship between energy and momentum is different for massive and massless particles. For massive particles,
while for massless particles,
where is the mass of the particle and is the speed of light. Using these relationships,
- For massive particles
where Λ is the thermal wavelength of the gas.
This is an important quantity, since when Λ is on the order of the inter-particle distance 1/3, quantum effects begin to dominate and the gas can no longer be considered to be a Maxwell-Boltzmann gas.
- For massless particles
where Λ is now the thermal wavelength for massless particles.
Specific examples
The following sections give an example of results for some specific cases.
Massive Maxwell-Boltzmann particles
For this case:
Integrating the energy distribution function and solving for N gives
Substituting into the original energy distribution function gives
which are the same results obtained classically for the Maxwell-Boltzmann distribution. Further results can be found in the classical section of the article on the ideal gas.
Massive Bose-Einstein particles
For this case:
Integrating the energy distribution function and solving for N gives the particle number
where Lis(z) is the polylogarithm function and Λ is the thermal wavelength. The polylogarithm term must always be positive and real, which means its value will go from 0 to ζ(3/2) as z goes from 0 to 1. As the temperature drops towards zero, Λ will become larger and larger, until finally Λ will reach a critical value Λc where z=1 and
The temperature at which Λ=Λc is the critical temperature. For temperatures below this critical temperature, the above equation for the particle number has no solution. The critical temperature is the temperature at which a Bose-Einstein condensate begins to form. The problem is, as mentioned above, that the ground state has been ignored in the continuum approximation. It turns out, however, that the above equation for particle number expresses the number of bosons in excited states rather well, and thus:
where the added term is the number of particles in the ground state. (The ground state energy has been ignored.) This equation will hold down to zero temperature. Further results can be found in the article on the ideal Bose gas.
Massless Bose-Einstein particles (e.g. black body radiation)
For the case of massless particles, the massless energy distribution function must be used. It is convenient to convert this function to a frequency distribution function:
where Λ is the thermal wavelength for massless particles. The spectral energy density (energy per unit volume per unit frequency) is then
Other thermodynamic parameters may be derived analogously to the case for massive particles. For example, integrating the frequency distribution function and solving for N gives the number of particles:
The most common massless Bose gas is a photon gas in a black body. Taking the "box" to be a black body cavity, the photons are continually being absorbed and re-emitted by the walls. When this is the case, the number of photons is not conserved. In the derivation of Bose-Einstein statistics, when the restraint on the number of particles is removed, this is effectively the same as setting the chemical potential (μ) to zero. Furthermore, since photons have two spin states, the value of f is 2. The spectral energy density is then
which is just the spectral energy density for Planck's law of black body radiation. Note that the Wien distribution is recovered if this procedure is carried out for massless Maxwell-Boltzmann particles, which approximates a Planck's distribution for high temperatures or low densities.
In certain situations, the reactions involving photons will result in the conservation of the number of photons (e.g. light-emitting diodes, "white" cavities). In these cases, the photon distribution function will involve a non-zero chemical potential. (Hermann 2005)
Another massless Bose gas is given by the Debye model for heat capacity. This considers a gas of phonons in a box and differs from the development for photons in that the speed of the phonons is less than light speed, and there is a maximum allowed wavelength for each axis of the box. This means that the integration over phase space cannot be carried out to infinity, and instead of results being expressed in polylogarithms, they are expressed in the related Debye functions.
Massive Fermi-Dirac particles (e.g. electrons in a metal)
For this case:
Integrating the energy distribution function gives
where again, Lis(z) is the polylogarithm function and Λ is the thermal de Broglie wavelength. Further results can be found in the article on the ideal Fermi gas.
References
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My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - Template:Cite web