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{{redirect2|Clapeyron equation|Clapeyron's equation|a state equation|ideal gas law}}
The '''Clausius–Clapeyron relation''', named after [[Rudolf Clausius]]<ref name="clausius">{{cite journal |last=Clausius |first=R. |title=Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen |trans_title=On the motive power of heat and the laws which can be deduced therefrom regarding the theory of heat|journal=Annalen der Physik |volume=155 |issue= |pages=500–524 |year=1850 |url=http://gallica.bnf.fr/ark:/12148/bpt6k15164w/f518.image|doi=10.1002/andp.18501550403 |bibcode = 1850AnP...155..500C |language=German }}</ref> and [[Benoît Paul Émile Clapeyron]],<ref name="clapeyron">{{cite journal |last=Clapeyron |first=M. C. |url=http://gallica.bnf.fr/ark:/12148/bpt6k4336791/f157 |title=Mémoire sur la puissance motrice de la chaleur |journal=Journal de l'École polytechnique |volume=23 |issue= |pages=153–190 |year=1834 |id=ark:/12148/bpt6k4336791/f157 |language=French }}</ref> is a way of characterizing a discontinuous [[phase transition]] between two [[phases of matter]] of a single constituent. On a [[pressure]]–[[temperature]] (P–T) diagram, the line separating the two phases is known as the coexistence curve. The Clausius–Clapeyron relation gives the [[slope]] of the [[tangents]] to this curve. Mathematically,


:<math>\frac{\mathrm{d}P}{\mathrm{d}T} = \frac{L}{T\,\Delta v}, </math>


where <math>\mathrm{d}P/\mathrm{d}T</math> is the slope of the tangent to the coexistence curve at any point, <math>L</math> is the specific [[latent heat]], <math>T</math> is the [[temperature]], and <math>\Delta v </math> is the [[specific volume]] change of the phase transition.
If you prefer a joyful and content pet cat, then allow him to test any variety of cat climbing trees. Working out is required for a good pet cat and ascending is the perfect method for kitty of burning excess calories and stay toned.<br><br>Despite the fact that felines sleeping approximately 18 several hours per day, they nonetheless really need to manage, run after and step at home. Cat trees deliver crazy fun for frisky felines and also a cozy spot to rest when they are done playing.<br><br>It is recommended to consider items like on the market living space, amount of felines as well as the style from your kitten when selecting feline play areas. Cat furniture might be a basic kitty condominium or even a more advanced style resembling a plant with most perches. You have many alternatives to select from as ascending foliage are available in quite a few variations and dimensions.<br><br>Possibilities in Cat Trees :<br><br>- Tiny Trees and shrubs - Modest feline towers are perfect if you are lacking area in your residence or maybe if you don't need to undertake a lot of living space with kitten furniture. The Trixie Dreamworld Sisal Kitten Tower is really a awesome stream-lined bit of kitty household furniture suitable for modest spaces. It options 3 carpeted amounts and a lush pom pom game is included.<br><br>- The Petco Kitty Suite Cat Posting can also be a combination of kitty plant and condo. The bottom is 3 scratching posts top up to a condo but still another damaging submit topped with a carpeted patio area for your satisfaction of the felines. The smaller types range from about 24 ins to 36 in . large. Many adaptations of such modest cat trees exist presenting kitty with further living quarters along with a location to flex his claws.<br><br>- IVG can make this fun entertaining cat tree in beige and brown gentle new carpet. You will discover 4 dangling pom pom toys and games to incorporate extra curiosity to your cat. A awesome feature are definitely the primary facilitates of the tree which are marring content. In addition to the very best lounging place, there's yet another comfy cover up aside pit in which kitty can curl up and slumber.<br><br>- Channel Shrubs - Channel kitten playgrounds or plants are more expensive, but unquestionably present far more intersting functions to your cat. This PetPal Beige Multi-Stage condo is an ideal medium-size play ground. They have 6 sisal scratching blogposts, 2 napping packing containers a relaxing foundation plus a being seated perch. There's another dangling rope teaser in addition to a dangling kitten game added.<br><br>- Should you have a tad bit more space for additional stages of perform area then test something similar to the Trixie DreamWorld Mijas Cat Tree. It options two lounging networks, a kitten hammock as well as 2 circle barrels for perching or camouflaging in. It really is covered with designer label carpets and rugs and has a dangling gadget for leisure. The principle system for this plant is really a sisal itching post. At 51 inches great, it is fantastic for a number of cats and kittens to spend time playing on together with each other.<br><br>If neccessary, - This Petco Premium Tree Terrace will deliver your pet cats a dining room table very best perch every single -! There are a few wonderful developments to this particular feline tower much like the sisal damaging ramp, dangling feather gadget, spring season feather game, sisal hanging rope and also a comfy getting to sleep pack. Measurements are 58.6" H, 28.7" L, 35.8" W. Napping package is 7.5" W, 8.7" H. Pet cat table top perches are approximately 15"x13" and 2" serious.<br><br>- If you're seeking a serious excellent component of feline furniture designed in the united states, this 4 tier kitty condominium by IVG Stores is just the ticket. Built away from solid pine carpet, all and poles natural sisal rope, this 66" significant cat climbing tree could possibly be excellent for your household pets. Accessible in 9 various hues, you're positive to search for the proper look for your residence. The roomy sleeping parts and perches about this tree let significant felines or many modest cats enjoy snoozing and lounging in coziness. Lengths and widths are 66" H, 30" W, 28" L.<br><br>- Sizeable Plants<br><br>The big cat tree furniture provides an remarkable quantity of capabilities, for example:<br><br>* The Northern Us citizen Animal Stylish Kitty Luxurious Cat Tree with Two Storyline Condo is equally as the identity indicates. The bottom is often a roomy, two history condo covered with luxurious carpeting and also a relaxing outdoor patio. Top of the point itching publish provides a lower outdoor patio in addition to a very best veranda with plenty of space to claw, go up and cat sleep. It truly is even engrossed in catnip for extra kitty enjoyable.<br><br>* A Hidden Hollow cat tree is 56 ins high and is made for people that have limited space. Handcrafted with two treetop lounging systems, flooring gives comfort and ease for the kitty. It’s real wood structure and artificial ivy foliage provide the outdoors inside of for your distinctive kitty.<br><br>You could truly ruin your kitty with custom climbing up shrubs. You choose dimensions, amount of networks, external surfaces dealing with and you can now even style and design the plant to match your décor. Some one of a kind cat trees even appear like authentic shrubs.<br><br>Create Your Very own<br><br>You can actually create your own cat tree in case you have somewhat some time and thoughts. Selected details can help you find the correct cathouse options, such as:<br><br>- Amount of kittens and cats<br><br>- Quantity of place<br><br>- cat scratch post [[http://moderncatfurniture.org/cat-scratch-post/ visit the following site]] Long-lasting shrub or movable<br><br>- Sum of money<br><br>- Time frame<br><br>- Level of experience<br><br>You should possess a good basic that is broad plenty of to assist the upper concentrations without having tipping around. After getting a long lasting starting point, the features available are never-ending.<br><br>Cat trees are really a pleasurable method for your kitten to act on his or her normal instincts where you can exclusive host to thier own. Up high or lower very low your feline will probably be happy with regardless of what model you end up picking, so go on and locate the excellent feline playground for your fantastic family pet!
 
== Derivations ==
[[File:Phase-diag2.svg|thumb|300px|A typical phase diagram. The dotted green line gives the anomalous behavior of water. The Clausius–Clapeyron relation can be used to find the relationship between pressure and temperature along phase boundaries.]]
 
=== Derivation from state postulate ===
 
Using the [[state postulate]], take the specific entropy, <math>s</math>, for a homogeneous substance to be a function of specific volume <math>v</math> and temperature <math>T</math>.<ref name="Wark1988">{{cite book |last=Wark |first=Kenneth |title=Thermodynamics |origyear=1966 |edition=5th |year=1988 |publisher=McGraw-Hill, Inc. |location=New York, NY |isbn=0-07-068286-0 |chapter=Generalized Thermodynamic Relationships}}</ref>{{rp|508}}
 
:<math>\mathrm{d} s = \left(\frac{\partial s}{\partial v}\right)_T \mathrm{d} v + \left(\frac{\partial s}{\partial T}\right)_v \mathrm{d} T.</math>
 
During a phase change, the temperature is constant, so<ref name="Wark1988"/>{{rp|508}}
 
:<math>\mathrm{d} s = \left(\frac{\partial s}{\partial v}\right)_T \mathrm{d} v.</math>
 
Using the appropriate [[Maxwell relation]] gives<ref name="Wark1988"/>{{rp|508}}
 
:<math>\mathrm{d} s = \left(\frac{\partial P}{\partial T}\right)_v \mathrm{d} v.</math>
 
Since temperature and pressure are constant ''during a phase transition'', the derivative of pressure with respect to temperature is not a function of the specific volume.<ref name="CRNave2006">{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/pvtsur.html |title=PvT Surface for a Substance which Contracts Upon Freezing |accessdate=2007-10-16 |author=Carl Rod Nave |year=2006 |work=HyperPhysics |publisher=Georgia State University }}</ref><ref name="Cengel1998">{{cite book |last=Çengel |first=Yunus A. |authorlink= |coauthors=Boles, Michael A. |title=Thermodynamics – An Engineering Approach |origyear=1989 |edition=3rd |series=McGraw-Hill Series in [[Mechanical Engineering]] |year=1998 |publisher=McGraw-Hill |location=Boston, MA. |isbn=0-07-011927-9}}</ref>{{rp|57, 62 & 671}} Thus the partial derivative may be changed into a total derivative and be factored out when taking an integral from one phase to another,<ref name="Wark1988"/>{{rp|508}}
 
:<math>s_{\beta} - s_{\alpha} = \frac{\mathrm{d} P}{\mathrm{d} T} (v_{\beta} - v_{\alpha}),</math>
:<math>\frac{d P}{d T} = \frac {s_{\beta} - s_{\alpha}}{v_{\beta} - v_{\alpha}} = \frac {\Delta s}{\Delta v}.</math>
Here <math>\Delta s\equiv s_{\beta}-s_{\alpha}</math> and <math>\Delta v\equiv v_{\beta}-v_{\alpha}</math> are respectively the change in specific entropy and specific volume from the initial phase <math>\alpha</math> to the final phase <math>\beta</math>.
 
For a closed system undergoing an internally reversible process, the [[first law of thermodynamics|first law]] is
 
:<math>\mathrm{d} u = \delta q - \delta w = T\;\mathrm{d} s - P\;\mathrm{d} v.\,</math>
 
Using the definition of [[specific enthalpy]], <math>h,</math> and the fact that the temperature and pressure are constant, we have<ref name="Wark1988"/>{{rp|508}}
 
:<math>\mathrm{d} u + P \;\mathrm{d} v = d h = T\;\mathrm{d}s \Rightarrow \mathrm{d}s = \frac {\mathrm{d} h}{T} \Rightarrow \Delta s = \frac {\Delta h}{T}=\frac{L}{T}.</math>
 
After substitution of this result into the derivative of the pressure, one finds<ref name="Wark1988"/>{{rp|508}}<ref name="Salzman2001">{{cite web |url=http://www.chem.arizona.edu/~salzmanr/480a/480ants/clapeyro/clapeyro.html |title=Clapeyron and Clausius–Clapeyron Equations |accessdate=2007-10-11 |last=Salzman |first=William R. |date=2001-08-21 |work=Chemical Thermodynamics |publisher=University of Arizona |archiveurl=http://web.archive.org/web/20070607143600/http://www.chem.arizona.edu/~salzmanr/480a/480ants/clapeyro/clapeyro.html
|archivedate=2007-07-07}}</ref>
 
:<math>\frac{\mathrm{d} P}{\mathrm{d} T} = \frac {L}{T \Delta v}.</math>
This last equation is the Clapeyron equation.
 
=== Derivation from Gibbs–Duhem relation ===
 
Suppose two phases, <math>\alpha</math> and <math>\beta</math>, are in contact and at equilibrium with each other. Then the chemical potentials are related by <math>\mu_{\alpha} = \mu_{\beta}.</math> Along the coexistence curve, we also have <math>\mathrm{d}\mu_{\alpha} = \mathrm{d}\mu_{\beta}.</math>  We now use the [[Gibbs–Duhem]] relation
<math>\mathrm{d}\mu = M(-s\mathrm{d}T + v\mathrm{d}P)</math>, where <math>s</math> and <math>v</math> are, respectively, the specific [[entropy]] and specific volume and <math>M</math> is the molar mass, to obtain
 
:<math>-(s_{\beta}-s_{\alpha}) \mathrm{d}T + (v_{\beta}-v_{\alpha}) \mathrm{d}P = 0. \,</math>
 
Hence, rearranging, we have
 
:<math>\frac{\mathrm{d}P}{\mathrm{d}T} = \frac{s_{\beta}-s_{\alpha}}{v_{\beta}-v_{\alpha}}.</math>
 
From which the derivation continues as above.
 
===Ideal gas approximation at low temperatures===
 
When the transition is to a gas phase at temperatures much lower than the [[critical point (thermodynamics)|critical temperature]], the specific volume of the gas phase <math>v_{\mathrm{g}}</math> greatly exceeds that of the condensed phase <math>v_{\mathrm{c}}</math>, and so one may approximate <math>\Delta v =v_{\mathrm{g}}\left(1-\tfrac{v_{\mathrm{c}}}{v_{\mathrm{g}}}\right)\approx v_{\mathrm{g}}</math>. Furthermore, at low pressures, the gas may be approximated by the ideal gas law, so that <math>v_{\mathrm{g}} = R T / P,</math> where R is the [[Gas constant#Specific gas constant|specific gas constant]]. Thus,<ref name="Wark1988"/>{{rp|509}}
 
:<math>\frac{\mathrm{d} P}{\mathrm{d} T} = \frac {P L}{T^2 R}.</math>
 
This is the Clausius–Clapeyron equation.<ref name="Wark1988"/>{{rp|509}} In general, <math>L</math> varies along the coexistence curve as a function of temperature. However, if <math>L</math> is a constant, then
:<math>\frac {\mathrm{d} P}{P} = \frac {L}{R} \frac {\mathrm{d}T}{T^2},</math>
:<math>\int_{P_1}^{P_2}\frac{\mathrm{d}P}{P} = \frac {L}{R} \int \frac {\mathrm{d} T}{T^2}</math>
:<math>\left. \ln P\right|_{P=P_1}^{P_2} = -\frac{L}{R} \cdot \left.\frac{1}{T}\right|_{T=T_1}^{T_2}</math> or<ref name="Cengel1998"/>{{rp|672}}
:<math>\ln \frac {P_2}{P_1} = \frac {L}{R} \left ( \frac {1}{T_1} - \frac {1}{T_2} \right ).</math>
 
Here <math>(P_1,T_1)</math> and <math>(P_2,T_2)</math> are two points along the coexistence curve. These last equations are useful because they relate [[equilibrium vapor pressure|equilibrium]] or [[saturation vapor pressure]] and temperature to the [[latent heat]] of the phase change, ''without'' requiring specific volume data. Note that in this last equation, the subscripts 1 and 2 label different locations on the <math>P</math>–<math>T</math> coexistence curve, whereas in previous equations the subscripts <math>\alpha</math> and <math>\beta</math> label the phases on either side of the coexistence curve.
 
==Applications==
 
===Chemistry and chemical engineering===
For transitions between a gas and a condensed phase with the approximations described above, the expression may be rewritten as
: <math>\ln P = -\frac{L}{R}\left(\frac{1}{T}\right)+C.</math>
 
For a liquid-gas transition, <math>L</math> is the specific latent heat (or specific enthalpy) of vaporization, whereas for a solid-gas transition, <math>L</math> is the specific latent heat of [[Sublimation (chemistry)|sublimation]]. If the latent heat is known, then knowledge of one point on the coexistence curve determines the rest of the curve. Conversely, the relationship between <math>\ln P</math> and <math>1/T</math> is linear, and so [[linear regression]] is used to estimate the latent heat.
 
===Meteorology and climatology===
 
The Clausius–Clapeyron equation for water vapor in typical atmospheric conditions is
 
:<math> \frac{\mathrm{d}e_s}{\mathrm{d}T} = \frac{L_v(T) e_s}{R_v T^2} </math>
 
where:
*<math> e_s </math> is saturation  vapor pressure,
*<math>T</math> is a temperature,
*<math> L_v </math> is the specific latent heat of evaporation,
*<math>R_v </math> is water vapor gas constant.
 
The temperature dependence of the latent heat cannot be neglected in this application (see [[dew point]]). In this context, a very good approximation can usually be made using the August-Roche-Magnus formula (usually called the Magnus or Magnus-Tetens approximation, though this attribution is historically inaccurate<ref>M. G. Lawrence, "The relationship between relative humidity and the dew point temperature in moist air: A simple conversion and applications", Bull. Am. Meteorol. Soc., 86, 225-233, 2005</ref>):
 
:<math> e_s(T)= 6.1094 \exp \left( \frac{17.625T}{T+243.04} \right).</math>
 
<math> e_s(T)</math> is the equilibrium or saturation vapor pressure in hPa as a function of temperature <math>T</math> on the Celsius scale. Since there is only a weak dependence on temperature of the [[denominator]] of the [[exponent]], this equation shows that saturation water vapor pressure changes approximately [[exponential function|exponentially]] with <math>T</math>.
 
In practical terms, this equation determines that the water-holding capacity of the atmosphere increases by about 7% for every 1°C rise in temperature.<ref>IPCC, Climate Change 2007: Working Group I: The Physical Science Basis, "FAQ 3.2 How is Precipitation Changing ?", URL http://www.ipcc.ch/publications_and_data/ar4/wg1/en/faq-3-2.html</ref>
 
== Example ==
One of the uses of this equation is to determine if a phase transition will occur in a given situation.  Consider the question of how much pressure is needed to melt ice at a temperature <math>{\Delta T}</math> below 0°C. Note that water is unusual in that its change in volume upon melting is negative. We can assume
 
:<math> {\Delta P} = \frac{L}{T\,\Delta v} {\Delta T} </math>
 
and substituting in
 
: <math>L</math> = 3.34{{e|5}}&nbsp;J/kg (latent heat of fusion for water),
: <math>T</math> = 273&nbsp;[[Kelvin|K]] (absolute temperature), and
: <math>\Delta v </math> = −9.05{{e|−5}}&nbsp;m³/kg (change in specific volume from solid to liquid),
 
we obtain
 
:<math>\frac{\Delta P}{\Delta T} </math> = −13.5&nbsp;MPa/K.
 
To provide a rough example of how much pressure this is, to melt ice at −7&nbsp;°C (the temperature many [[ice skating]] rinks are set at) would require balancing a small car (mass = 1000&nbsp;kg<ref>{{cite web|url=http://hypertextbook.com/facts/2000/YanaZorina.shtml|title=Mass of a Car|last=Zorina|first=Yana|year=2000|work=The Physics Factbook}}</ref>) on a [[thimble]] (area = 1&nbsp;cm²).
 
==See also==
*[[Van 't Hoff equation]]
*[[Antoine equation]]
 
==References==
{{reflist}}
 
==Bibliography==
* M.K. Yau and R.R. Rogers, ''Short Course in Cloud Physics, Third Edition'', published by Butterworth–Heinemann, January 1, 1989, 304 pages. EAN 9780750632157 ISBN 0-7506-3215-1
* J.V. Iribarne and W.L. Godson, ''Atmospheric Thermodynamics'', published by D. Reidel Publishing Company, [[Dordrecht]], [[Holland]], 1973, 222 pages
* H.B. Callen, ''Thermodynamics and an Introduction to Thermostatistics'', published by Wiley, 1985.  ISBN 0-471-86256-8
 
{{DEFAULTSORT:Clausius-Clapeyron Relation}}
[[Category:Thermodynamics]]
[[Category:Atmospheric thermodynamics]]
[[Category:Chemical engineering]]

Latest revision as of 00:20, 26 November 2014


If you prefer a joyful and content pet cat, then allow him to test any variety of cat climbing trees. Working out is required for a good pet cat and ascending is the perfect method for kitty of burning excess calories and stay toned.

Despite the fact that felines sleeping approximately 18 several hours per day, they nonetheless really need to manage, run after and step at home. Cat trees deliver crazy fun for frisky felines and also a cozy spot to rest when they are done playing.

It is recommended to consider items like on the market living space, amount of felines as well as the style from your kitten when selecting feline play areas. Cat furniture might be a basic kitty condominium or even a more advanced style resembling a plant with most perches. You have many alternatives to select from as ascending foliage are available in quite a few variations and dimensions.

Possibilities in Cat Trees :

- Tiny Trees and shrubs - Modest feline towers are perfect if you are lacking area in your residence or maybe if you don't need to undertake a lot of living space with kitten furniture. The Trixie Dreamworld Sisal Kitten Tower is really a awesome stream-lined bit of kitty household furniture suitable for modest spaces. It options 3 carpeted amounts and a lush pom pom game is included.

- The Petco Kitty Suite Cat Posting can also be a combination of kitty plant and condo. The bottom is 3 scratching posts top up to a condo but still another damaging submit topped with a carpeted patio area for your satisfaction of the felines. The smaller types range from about 24 ins to 36 in . large. Many adaptations of such modest cat trees exist presenting kitty with further living quarters along with a location to flex his claws.

- IVG can make this fun entertaining cat tree in beige and brown gentle new carpet. You will discover 4 dangling pom pom toys and games to incorporate extra curiosity to your cat. A awesome feature are definitely the primary facilitates of the tree which are marring content. In addition to the very best lounging place, there's yet another comfy cover up aside pit in which kitty can curl up and slumber.

- Channel Shrubs - Channel kitten playgrounds or plants are more expensive, but unquestionably present far more intersting functions to your cat. This PetPal Beige Multi-Stage condo is an ideal medium-size play ground. They have 6 sisal scratching blogposts, 2 napping packing containers a relaxing foundation plus a being seated perch. There's another dangling rope teaser in addition to a dangling kitten game added.

- Should you have a tad bit more space for additional stages of perform area then test something similar to the Trixie DreamWorld Mijas Cat Tree. It options two lounging networks, a kitten hammock as well as 2 circle barrels for perching or camouflaging in. It really is covered with designer label carpets and rugs and has a dangling gadget for leisure. The principle system for this plant is really a sisal itching post. At 51 inches great, it is fantastic for a number of cats and kittens to spend time playing on together with each other.

If neccessary, - This Petco Premium Tree Terrace will deliver your pet cats a dining room table very best perch every single -! There are a few wonderful developments to this particular feline tower much like the sisal damaging ramp, dangling feather gadget, spring season feather game, sisal hanging rope and also a comfy getting to sleep pack. Measurements are 58.6" H, 28.7" L, 35.8" W. Napping package is 7.5" W, 8.7" H. Pet cat table top perches are approximately 15"x13" and 2" serious.

- If you're seeking a serious excellent component of feline furniture designed in the united states, this 4 tier kitty condominium by IVG Stores is just the ticket. Built away from solid pine carpet, all and poles natural sisal rope, this 66" significant cat climbing tree could possibly be excellent for your household pets. Accessible in 9 various hues, you're positive to search for the proper look for your residence. The roomy sleeping parts and perches about this tree let significant felines or many modest cats enjoy snoozing and lounging in coziness. Lengths and widths are 66" H, 30" W, 28" L.

- Sizeable Plants

The big cat tree furniture provides an remarkable quantity of capabilities, for example:

* The Northern Us citizen Animal Stylish Kitty Luxurious Cat Tree with Two Storyline Condo is equally as the identity indicates. The bottom is often a roomy, two history condo covered with luxurious carpeting and also a relaxing outdoor patio. Top of the point itching publish provides a lower outdoor patio in addition to a very best veranda with plenty of space to claw, go up and cat sleep. It truly is even engrossed in catnip for extra kitty enjoyable.

* A Hidden Hollow cat tree is 56 ins high and is made for people that have limited space. Handcrafted with two treetop lounging systems, flooring gives comfort and ease for the kitty. It’s real wood structure and artificial ivy foliage provide the outdoors inside of for your distinctive kitty.

You could truly ruin your kitty with custom climbing up shrubs. You choose dimensions, amount of networks, external surfaces dealing with and you can now even style and design the plant to match your décor. Some one of a kind cat trees even appear like authentic shrubs.

Create Your Very own

You can actually create your own cat tree in case you have somewhat some time and thoughts. Selected details can help you find the correct cathouse options, such as:

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- Quantity of place

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- Sum of money

- Time frame

- Level of experience

You should possess a good basic that is broad plenty of to assist the upper concentrations without having tipping around. After getting a long lasting starting point, the features available are never-ending.

Cat trees are really a pleasurable method for your kitten to act on his or her normal instincts where you can exclusive host to thier own. Up high or lower very low your feline will probably be happy with regardless of what model you end up picking, so go on and locate the excellent feline playground for your fantastic family pet!

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