• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Charged torus-like black holes as heat engines

    2021-04-28 02:27:06HanwenFengYuchenHuangWeiHongandJunTao
    Communications in Theoretical Physics 2021年4期

    Hanwen Feng,Yuchen Huang,Wei Hongand Jun Tao

    Center for Theoretical Physics,College of Physics,Sichuan University,Chengdu,610064,China

    Abstract We investigate the thermodynamical properties of charged torus-like black holes and take it as the working substance to study the heat engines.In the extended phase space,by interpreting the cosmological constant as the thermodynamic pressure,we derive the thermodynamical quantities by the first law of black hole thermodynamics and obtain the equation of state.Then,we calculate the efficiency of the heat engine in the Carnot cycle as well as the rectangular cycle,and investigate how the efficiency changes with respect to volume.In addition,to avoid a negative temperature,we emphasize that the charge of this black hole cannot be arbitrary.Last,we check the calculation accuracy of a benchmark scheme and discuss the upper bound and lower bound for charged torus-like black hole in the scheme.

    Keywords: charged torus-like black holes,heat engines,benchmark scheme

    1.Introduction

    The pioneering work of Hawking and Bekenstein [1–4] stimulates the interest in the study of black hole thermodynamics.Hawking temperature and Bekenstein–Hawking entropy provides a profound insight into the nature of quantum gravity.In the extended framework,the cosmological constant is considered as a dynamical parameter and the mass of an Anti-de Sitter(AdS)black hole can be interpreted as the enthalpy of the space [5,6].Compared with the classical thermodynamic,people have gradually established four laws of black hole thermodynamics.

    The holographic principle is developed from the Bekenstein–Hawking entropy,while the thermodynamic behaviour of black holes in AdS space reveals the strong coupling gauge theory through various proposed dualities[7].Based on this assumption,Johnson proposed a heat engine defined in the extended thermodynamical space,which takes the AdS black holes as the working substance[8].For a negative cosmological constant,the engine cycle corresponds to a process defined on the space of dual field theories.To understand the holographic heat engine,it is rather important to investigate the microscopic structure.Many different theories have been studied to explore the microscopic property of black holes [9–14].For further investigation,a concept,i.e.the number density n of the virtual black hole molecules,is introduced to study the behaviours of the microscopic thermodynamic variables[15,16].It can be regarded as the order parameter to measure the microscopic degrees of freedom and it is related to the size or radius of the black hole[17].From this point,we can take the process of a black hole doing work as the changes in n,but it remains a conception and still requires more effort to understand the microscopic structure.

    The heat engine is defined in the P–V space as a closed path.At first,we can calculate the efficiency of the holographic heat engines of black holes with vanishing specific heat at constant volume (CV=0) in analytical way.Next,Johnson investigated the efficiency of Born–Infeld black hole in the rectangular cycle [18] and then obtained a efficiency formula for heat engines in this rectangular cycle [19,20].When the engine is defined as a rectangular cycle expressed with mass and internal energy of the black hole,the calculation for black holes with CV≠0 is capable as well [21].Since various black holes can be the working substance of a heat engine,and the efficiency is a dimensionless quantity,we can compare different black holes’ efficiency and investigate their thermodynamical properties further.To avoid the case where one particular heat engine yields advantages for one specific black hole,Chakraborty and Johnson proposed the benchmarking scheme [22,23],which separates a complicated cycle into rectangular cycles and calculates the efficiency approximately with numerical method.Recently,black holes in massive gravity have been discussed as heat engines in [24–26].Then,researchers have studied the thermodynamics and heat engine efficiency of charged accelerating AdS black holes [27,28],nonlinear black holes [29,30] and the general class of accelerating,rotating and charged Plebanski–Demianski black holes[30].Moreover,Johnson have investigated the de sitter Black holes in [32].More work on heat engines can be found in [33–43].

    In this paper,we investigate the heat engine efficiency of the torus-like black hole in Carnot cycle,rectangular cycle and the benchmark cycle.The torus-like black hole is a static solution of the Einstein-Maxwell equation,whose event horizon hasS1×S1× R topology [44–48].Each surface of this black hole of the spacetime at constant radius has a toroidal topology which is different from that of the asymptotically flat spacetimes.

    This paper is organized as follows.In section 2,we investigate the thermodynamic property of a torus-like black hole and derive the expression for thermodynamic quantities.In section 3,we construct a rectangular heat engine cycle,and then take the torus-like black hole as the working substance to study its efficiency with respect to volume.Since the Carnot heat engine is theoretically with the maximum efficiency,we compare it with the rectangular engine to check.In section 4,we calculate the efficiency of benchmark cycle and investigate how the upper bound limits the charge.In the end,the conclusion is given in section 5.

    2.Thermodynamics of charged torus-like black hole

    We are interested in charged torus-like black hole,the ansatz for metric can be written as [44],

    with

    where M and Q are mass and electric charge of the black hole,Λ is the cosmological constant.The black hole mass can be obtained by f(r+)=0,where r+is the event horizon radius,

    In 4D AdS spacetime,the negative cosmological constant can be considered as thermodynamical pressure with[5],so that M can be rewritten as

    The variation of the mass takes on the form

    According to the definition of surface gravity,the Hawking temperature is only related to the black hole metric[48],

    Substituting equation (4) into (6),the temperature can be written as

    With the relation between the Bekenstein–Hawking entropy and the surface area of the event horizon,the entropy of this black hole can be expressed as

    The thermodynamic volume and electric potential at the event horizon are given by

    In the extended thermodynamics,the mass of an AdS black hole is interpreted to the enthalpy of spacetime [5].And equations (5)–(9) shows the first law of thermodynamics is satisfied,

    As the entropy and volume are both the function of black holes horizon,the heat capacity at constant volume vanishes,

    The state equation of the black hole can be derived from equations (7) and (9),

    As the critical point satisfies the condition that the first-order partial derivative with respect to volume of pressure and the second-order partial derivative are 0,we derive these two partial derivatives to find this point

    From equation(13),we can see thatis not feasible as the square term,temperature and volume are always positive.This result indicates the absence of critical point as shown in figure 1,and correspondingly,this black hole has no secondorder phase transition [49].

    For the purpose of studying the behaviour of torus-like black hole as a heat engine,we prefer writing the enthalpy M entirely in terms of P and V by substituting equation (9) into(4),and then the expression yields:

    Figure 1.The figure shows P versus V for different temperature.Here Q is fixed at 1.

    It should be noted that,when the torus-like black hole carries no electric charge,i.e.Q=0,its enthalpy M reduces to the same form as that of ideal gas,namely M=PV [22],which will be discussed later.

    3.Charged torus-like black hole as a heat engine

    Since the equation of state for the charged black hole is obtained,we could discuss further by considering this black hole as a heat engine and calculating its efficiency.In the following sections,the black hole is set in thermodynamical cycles and produces work via the PdV term.We denote the heat absorbed as QH,and the heat exhausted as QC,so that the mechanical work is W=QH?QC.The efficiency is the ratio of mechanical work W to heat absorbed QH[24],

    The Carnot cycle consists of two isothermal paths and two adiabatic paths and has the highest efficiency.Note that for the black hole engine,the entropy remains constant if the volume does not change,so the adiabatic path is equivalent to the isochoric path.Moreover,we define a rectangular cycle with two isochoric and two isobaric paths and compare its efficiency with that of Carnot cycle.We compare the diagram of the two cycles in figure 2.

    The Carnot heat engine is between two different temperatures,we define the higher temperature as THand the lower one as TL,which are connected through the isochoric paths.We can know from figure 2 that TH=T1=T2,TL=T3=T4,V1=V4and V2=V3for Carnot cycle.The heat QHand QCcan be calculated in the process of isothermal expansion and compression [24],

    Since the volume is connected through isochoric paths,the expression for heat engine efficiency in equation (15) can be written as:

    In order to investigate the relationship between efficiency and volume,one can substitute equations (3) and (9) into (6),the temperature could be rewritten as,

    Then we can obtain the efficiency of Carnot engine,

    Using the above formula to compute Carnot heat engine efficiency with the volume of this black hole is straightforward.Here we choose parameters P2=4,P4=1 and V2=4,V4=1,with different charge Q.Then we can plot the efficiency of Carnot cycle versus the black hole volume V2in figure 3.It shows the efficiency increases monotonously and flattens out with the increase of volume.Note that for a larger volume,the corresponding efficiency is higher.

    It should be noted that the temperature cannot be negative,otherwise it makes no sense in physics,so that the charge Q is not arbitrary.Considering the extremal black hole situation T=0,the maximum charge reads,

    We can set P1=P2=4,P3=P4=1,V1=V4=1,and V2=V3=4,after taking both the lower temperature and the higher one into account,the charge of black hole is restricted as ?0.797Q0.797 to make the expression physical.We can plot the efficiency changing with the varying charge in figure 4.There are two cut-off pointsQc1=0.797andQc2= ?0.797in the curve,when charge Q reaches the limitation,the black hole temperature T=0 and the heat engine efficiency η=1.The cut-off point here reveals the information of Hawking temperature and corresponds to the extremal black holes.Besides,it can be seen from the figure 4 that the efficiency of the Carnot heat engine has a minimum value,if the torus-like black hole carries no electric charge.

    As we will see,the rectangular cycle is the most natural cycle to consider for all AdS black holes,because it can be generalized to an algorithm,which allows more complex cycles to be numerically calculated.The rectangular cycle goes through isobaric and isochoric paths,although there are four states in the cycle,we can set P1=P2,P3=P4,V1=V4,V2=V3as shown in figure 2.The heat engine efficiency for the rectangle cycle can be calculated by a formula deduced in [19,20],

    where

    Figure 2.The thermodynamical cycles.

    Figure 3.The heat engine efficiency of Carnot cycle versus the black hole volume V2 for different charge Q,where we set V4=1,P2=4,and P4=1.

    Figure 4.The Carnot heat engine efficiency with varying charge Q.

    According to equation (22),we can choose parameters P1=P2=4,P4=1 and V1=V4=1,and then we plot the heat engine efficiency of rectangle cycle with respect to the volume V2with different charge Q in figure 5.It is obvious that when the charge is fixed,the efficiency curve flattens out as the volume increases and tends to a stable value.Meanwhile,the larger volume V2leads to a lower efficiency,which differs from the situation for the Carnot cycle we mentioned above.On the other hand,for the same volume,the larger Q results in higher efficiency both for Carnot cycle and rectangular cycle.

    Figure 5.The engine efficiency of rectangle cycle versus the black hole volume V2,with parameters set same as the Carnot cycle.

    4.The benchmark cycle for charged torus-like black hole

    In this section,we introduce a benchmark cycle [22],which could be parameterised as a circle.The scheme is adequately complicated as the thermodynamic variables changes on every segment of the cycle,and thus it is more general than regular cycles.This research method can be applied to compare the heat engine efficiency of different black holes.In addition,an upper bound is obtained in [21] which indicates the efficiency of this cycle is always lower than a specific value.

    Generally,the heat engine efficiency is calculated by numerical method.To simplify our calculation,we choose a circular cycle with center of which set as (Po,Vo) and radius as R.We overlay our circular cycle onto the N×N regular lattice of squares,and we require N to be even for simplicity.The side length of every square is 2L/N,which ensures those squares can cover the circle.Next we check the cases where two squares share a common isobar and it intersects the circle.Then we calculate the ΔM of the left and right endpoints of the isobar.

    Figure 6.Efficiency of the charged torus-like black hole calculated with the numerical method.Here we set the circle origin at Vo=110 and Po=20,the charge Q=20.0 and radius R=10.0.The efficiency equals to 0.587 226 when N=500.

    The heat input QHwill be the sum of ΔM in the upper semicircle and the heat output QCis given by the sum of ΔM in the lower semicircle.Thus we can calculate the efficiency with the numerical method [22]

    where,

    The result converges to the right value with a larger N,as it makes the square smaller and thus fit to the circle more perfectly.Figure 6 shows that as N increases,the efficiency approaches to an exact result.

    In a particular case where the specific heat capacity at constant volume CV=0,we can calculate the efficiency in an analytical way.Then we can check the the accuracy of the above numerical method by comparing it with an analytical method.The heat engine efficiency would be [21]

    where ΔM is the enthalpy difference of two points at the left and right ends of the circle,

    By substituting those parameters of figure 6 into equation (26),we obtain the analytical result ηa=0.589 322.Comparing with the results of numerical method when N reaches 500,ηn=0.587 226,we can conclude that the error of the numerical method is within the acceptable range and the scheme can be applied to the case where analytical method does not work.

    Figure 7.This figure plots the efficiency of two black holes with respect to Q in the benchmark cycle.

    In the benchmark scheme,an upper bound for the efficiency of black holes with CV=0 in circular cycles with the narrow cycle limit and low temperature limit is obtained[21],

    It is independent of both theory and spacetime dimension,with equality obtained for extremal black holes in the small cycle limit.

    As we mentioned earlier,when the black hole charge Q=0,its enthalpy M is the same as that of ideal gas[22],and we can get the lower limit of the efficiency of the torus-like black hole heat engine.The efficiency of ideal gas is independent of V and spacetime and only depends on the pressure at the center of the cycle and the radius of the circle,as mentioned in [18,22,23]

    We conclude the consideration of benchmarking of the black hole heat engines,and present it in figure 7.The efficiency of ideal gas model is 0.5639 at P=20.0 and R=10.0.When Q=57.7431,η reaches the extremal limit 0.8798.As equation(14)shows,the mass of torus-like black hole has the same form as the ideal gas when the black hole carries no charge,so the efficiency curve of the black hole and the ideal gas start at the exact point.On the other hand,the top horizontal line is the extremal limit,and it forbids the efficiency to exceed itself.

    5.Conclusion

    In this paper,we have studied the thermodynamical behaviour of charged torus-like black hole in the extended phase space.By considering the cosmological constant in AdS space as the thermodynamical pressure and the mass as the enthalpy in the first law of thermodynamics,we can obtain all the thermodynamical quantities and the relationship between them.We derive the equation of state with thermodynamical quantities and find there does not exist a critical point in the phase diagram which represents the absence of phase transition.

    Then,we considered charged torus-like black hole as a working substance and studied the holographic heat engine by Carnot cycle and rectangular cycle.The Carnot cycle consists of two isothermal paths and two adiabatic paths,it is always theoretically highest according to the second law of thermodynamics,and thus it provides an upper bound for us to check the calculation.The rectangular cycle is made up of two isochoric paths and two isobaric paths.It works for all black holes,not requiring the specific heat capacity CV=0,and it could be an operation unit in other cycles and enable us to calculate the efficiency of the benchmark cycle with numerical methods.From figures 5 and 3,we conclude that the rectangular efficiency decreases monotonously with respect to the difference between the volume at initial and final states,while the Carnot efficiency does the opposite.

    The heat engine cycle in the benchmark scheme is more complicated,and we differentiate the curve into line segments and calculate the efficiency approximately.We compare the numerical result with the analytical result and check the calculation accuracy of numerical methods,then we find the error is acceptable.Due to the fact that the torus-like black hole has the same enthalpy with the ideal gas when Q=0 and that Q increases the efficiency,the efficiency of ideal gas is a lower bound for the torus-like black hole.On the other hand,the efficiency of a certain class of asymptotically AdS black holes with CVin the circular cannot exceed a upper bound as well.

    Acknowledgments

    We are grateful to thank Peng Wang and Feiyu Yao for useful discussions.This work is supported by NSFC (Grant No.11947408).

    ORCID iDs

    久久热在线av| 听说在线观看完整版免费高清| 国产精品亚洲美女久久久| 国产成人av激情在线播放| 免费在线观看日本一区| 欧美一级a爱片免费观看看 | 99热这里只有是精品50| 免费看日本二区| 99在线人妻在线中文字幕| 在线观看舔阴道视频| www国产在线视频色| 国产熟女午夜一区二区三区| 国产亚洲av嫩草精品影院| 亚洲一卡2卡3卡4卡5卡精品中文| 麻豆国产av国片精品| 国模一区二区三区四区视频 | 人妻夜夜爽99麻豆av| 国产精品亚洲av一区麻豆| 精品久久久久久成人av| 九色国产91popny在线| 黑人操中国人逼视频| 亚洲专区国产一区二区| 在线观看www视频免费| 老熟妇仑乱视频hdxx| 三级国产精品欧美在线观看 | 日韩欧美 国产精品| 成人精品一区二区免费| 中文资源天堂在线| 午夜成年电影在线免费观看| 黄色丝袜av网址大全| 国产成人精品无人区| 国产不卡一卡二| 国产三级在线视频| 在线观看舔阴道视频| 欧美精品啪啪一区二区三区| 91九色精品人成在线观看| 色av中文字幕| 亚洲五月天丁香| 俺也久久电影网| 香蕉丝袜av| 91av网站免费观看| 岛国视频午夜一区免费看| 国模一区二区三区四区视频 | 看免费av毛片| 国内精品久久久久精免费| 麻豆一二三区av精品| 桃色一区二区三区在线观看| 亚洲成av人片免费观看| 国产区一区二久久| 精品第一国产精品| 亚洲在线自拍视频| 精品国内亚洲2022精品成人| 女人爽到高潮嗷嗷叫在线视频| 精品不卡国产一区二区三区| 免费看a级黄色片| 亚洲精品色激情综合| 香蕉丝袜av| 黄片大片在线免费观看| 俺也久久电影网| tocl精华| 国产精品一区二区三区四区久久| 欧美日韩乱码在线| 国产亚洲欧美98| 久久天躁狠狠躁夜夜2o2o| 毛片女人毛片| 亚洲成人精品中文字幕电影| 午夜福利在线在线| 18禁黄网站禁片免费观看直播| 婷婷精品国产亚洲av在线| 色在线成人网| 午夜视频精品福利| 欧美精品啪啪一区二区三区| 午夜亚洲福利在线播放| 丰满人妻一区二区三区视频av | 国产精品久久视频播放| 亚洲,欧美精品.| 欧美日韩乱码在线| 亚洲av第一区精品v没综合| 免费人成视频x8x8入口观看| 亚洲av熟女| 久久久国产成人免费| 人妻久久中文字幕网| 最近在线观看免费完整版| cao死你这个sao货| 亚洲色图av天堂| 男插女下体视频免费在线播放| 国内揄拍国产精品人妻在线| 波多野结衣高清无吗| 最好的美女福利视频网| 国产一区二区在线观看日韩 | a在线观看视频网站| 成年人黄色毛片网站| 一进一出抽搐动态| 两人在一起打扑克的视频| 性欧美人与动物交配| 国产单亲对白刺激| 欧美最黄视频在线播放免费| 欧美 亚洲 国产 日韩一| www日本在线高清视频| 国产黄片美女视频| 国产精品影院久久| 少妇被粗大的猛进出69影院| 99精品欧美一区二区三区四区| 99久久无色码亚洲精品果冻| 在线观看日韩欧美| 婷婷丁香在线五月| 99热这里只有精品一区 | 午夜精品一区二区三区免费看| 熟女少妇亚洲综合色aaa.| av福利片在线| 日本在线视频免费播放| 亚洲男人的天堂狠狠| 国产精品久久视频播放| 精品无人区乱码1区二区| 欧美日韩福利视频一区二区| 免费看日本二区| 丝袜人妻中文字幕| 亚洲人成伊人成综合网2020| 日本在线视频免费播放| 一个人免费在线观看的高清视频| 无限看片的www在线观看| 在线十欧美十亚洲十日本专区| 国产99白浆流出| 亚洲成人精品中文字幕电影| 精品少妇一区二区三区视频日本电影| 午夜两性在线视频| 嫩草影视91久久| 亚洲国产精品999在线| 亚洲国产欧洲综合997久久,| 精品久久久久久久毛片微露脸| 男女视频在线观看网站免费 | 欧美黑人欧美精品刺激| 国产一区二区在线观看日韩 | 天堂av国产一区二区熟女人妻 | 国产午夜福利久久久久久| 美女午夜性视频免费| 99国产综合亚洲精品| 国产麻豆成人av免费视频| 黄色丝袜av网址大全| 淫妇啪啪啪对白视频| 老熟妇乱子伦视频在线观看| 国内少妇人妻偷人精品xxx网站 | 亚洲自拍偷在线| 欧美在线黄色| 在线免费观看的www视频| 亚洲国产看品久久| 亚洲,欧美精品.| 国产亚洲欧美在线一区二区| 黄色视频,在线免费观看| 19禁男女啪啪无遮挡网站| 久久久精品欧美日韩精品| 国产在线观看jvid| 丁香六月欧美| 看黄色毛片网站| 一级黄色大片毛片| 日韩精品青青久久久久久| 亚洲乱码一区二区免费版| 日韩 欧美 亚洲 中文字幕| 老熟妇乱子伦视频在线观看| 欧美性猛交╳xxx乱大交人| 婷婷六月久久综合丁香| 九九热线精品视视频播放| 一夜夜www| 亚洲av电影在线进入| 最近最新中文字幕大全免费视频| 成在线人永久免费视频| 曰老女人黄片| 亚洲中文字幕日韩| 久久欧美精品欧美久久欧美| 久久中文看片网| 在线观看午夜福利视频| 婷婷丁香在线五月| 午夜精品一区二区三区免费看| 国产精品亚洲一级av第二区| avwww免费| 色播亚洲综合网| xxxwww97欧美| 久久人妻av系列| 色老头精品视频在线观看| 老司机靠b影院| 国产精品久久久久久久电影 | 亚洲av电影在线进入| 日本a在线网址| 国产人伦9x9x在线观看| av有码第一页| 久久久久久大精品| 欧美黄色片欧美黄色片| 母亲3免费完整高清在线观看| 成年人黄色毛片网站| 欧美日韩亚洲国产一区二区在线观看| 成人永久免费在线观看视频| 成人特级黄色片久久久久久久| 国产午夜福利久久久久久| 波多野结衣巨乳人妻| 久久精品91无色码中文字幕| 亚洲国产欧美一区二区综合| 精品久久蜜臀av无| 久久精品亚洲精品国产色婷小说| 黄色 视频免费看| 人人妻人人澡欧美一区二区| 琪琪午夜伦伦电影理论片6080| 制服诱惑二区| 99热这里只有精品一区 | 一进一出抽搐gif免费好疼| 啦啦啦观看免费观看视频高清| 精品国内亚洲2022精品成人| 又黄又粗又硬又大视频| 国产三级中文精品| 99国产综合亚洲精品| x7x7x7水蜜桃| 黄色毛片三级朝国网站| ponron亚洲| 精品不卡国产一区二区三区| 亚洲五月天丁香| 午夜精品在线福利| 日本在线视频免费播放| 又紧又爽又黄一区二区| 99re在线观看精品视频| 久久精品国产亚洲av香蕉五月| 午夜福利高清视频| 欧美黄色片欧美黄色片| 久久精品91无色码中文字幕| 色综合欧美亚洲国产小说| 好看av亚洲va欧美ⅴa在| 国内少妇人妻偷人精品xxx网站 | 少妇粗大呻吟视频| 国产又色又爽无遮挡免费看| 91成年电影在线观看| а√天堂www在线а√下载| 日韩欧美在线二视频| 首页视频小说图片口味搜索| 日本一本二区三区精品| 人妻丰满熟妇av一区二区三区| 欧美另类亚洲清纯唯美| 成人精品一区二区免费| 老熟妇乱子伦视频在线观看| 国产又色又爽无遮挡免费看| 精华霜和精华液先用哪个| 国内精品一区二区在线观看| 又粗又爽又猛毛片免费看| 村上凉子中文字幕在线| 男女午夜视频在线观看| 天堂av国产一区二区熟女人妻 | 久久久久久大精品| 国产不卡一卡二| 欧美一级a爱片免费观看看 | 窝窝影院91人妻| 成人一区二区视频在线观看| 在线视频色国产色| 极品教师在线免费播放| 91麻豆av在线| 亚洲国产欧美网| 悠悠久久av| 男女下面进入的视频免费午夜| 亚洲,欧美精品.| 丰满人妻一区二区三区视频av | 婷婷精品国产亚洲av| 可以在线观看的亚洲视频| 日本一二三区视频观看| 搡老妇女老女人老熟妇| 欧美在线一区亚洲| 桃色一区二区三区在线观看| 久久久久国产一级毛片高清牌| av超薄肉色丝袜交足视频| 精品一区二区三区av网在线观看| 一个人观看的视频www高清免费观看 | 最近最新中文字幕大全电影3| 亚洲aⅴ乱码一区二区在线播放 | 久久精品人妻少妇| 欧美日本亚洲视频在线播放| 老汉色∧v一级毛片| 99re在线观看精品视频| 久久久精品欧美日韩精品| 青草久久国产| 黄片大片在线免费观看| 久久久久性生活片| 人妻久久中文字幕网| 久久久久免费精品人妻一区二区| 国产精品久久久久久久电影 | 精品国产乱码久久久久久男人| 欧美黄色片欧美黄色片| 亚洲av熟女| 精品日产1卡2卡| 久久久精品大字幕| 黄色成人免费大全| 日韩欧美国产一区二区入口| 中文亚洲av片在线观看爽| 天天躁夜夜躁狠狠躁躁| 国产在线观看jvid| 一级a爱片免费观看的视频| 色噜噜av男人的天堂激情| 日韩精品免费视频一区二区三区| 久久久久久久久久黄片| 久久精品aⅴ一区二区三区四区| 国内毛片毛片毛片毛片毛片| 国产精品av视频在线免费观看| 亚洲av电影在线进入| 国产麻豆成人av免费视频| 亚洲av成人精品一区久久| 天天一区二区日本电影三级| av在线播放免费不卡| 亚洲国产欧美人成| 18禁裸乳无遮挡免费网站照片| 制服人妻中文乱码| 天天一区二区日本电影三级| 亚洲精品一区av在线观看| 宅男免费午夜| 性色av乱码一区二区三区2| 夜夜夜夜夜久久久久| 超碰成人久久| 婷婷精品国产亚洲av在线| 久久精品影院6| 99久久精品国产亚洲精品| 亚洲国产日韩欧美精品在线观看 | 久久天躁狠狠躁夜夜2o2o| 天堂影院成人在线观看| 可以在线观看毛片的网站| 午夜两性在线视频| 国产高清视频在线播放一区| 久久精品91蜜桃| 欧美日本亚洲视频在线播放| 黄频高清免费视频| 18禁黄网站禁片午夜丰满| 国产av一区在线观看免费| 国产精品亚洲一级av第二区| or卡值多少钱| 国产日本99.免费观看| 国产精品一区二区三区四区免费观看 | 亚洲男人的天堂狠狠| 天堂av国产一区二区熟女人妻 | 国产午夜精品论理片| 婷婷精品国产亚洲av在线| 1024视频免费在线观看| 最新在线观看一区二区三区| 精品久久久久久久久久久久久| 嫁个100分男人电影在线观看| 俄罗斯特黄特色一大片| bbb黄色大片| 狂野欧美激情性xxxx| 黄色 视频免费看| 757午夜福利合集在线观看| 动漫黄色视频在线观看| 亚洲精品美女久久久久99蜜臀| 亚洲性夜色夜夜综合| 桃红色精品国产亚洲av| 50天的宝宝边吃奶边哭怎么回事| 又黄又爽又免费观看的视频| 国产av一区二区精品久久| 亚洲18禁久久av| 两个人视频免费观看高清| 国产成人欧美在线观看| 麻豆一二三区av精品| 亚洲成人久久性| 日韩成人在线观看一区二区三区| 亚洲18禁久久av| 久久这里只有精品19| 淫妇啪啪啪对白视频| 午夜免费成人在线视频| 美女高潮喷水抽搐中文字幕| 丝袜美腿诱惑在线| 亚洲国产精品久久男人天堂| 成人高潮视频无遮挡免费网站| 国产私拍福利视频在线观看| 一夜夜www| 日韩大尺度精品在线看网址| 亚洲精品一卡2卡三卡4卡5卡| 国产一区二区在线av高清观看| 操出白浆在线播放| 国产免费男女视频| 国产男靠女视频免费网站| 国产欧美日韩精品亚洲av| 桃色一区二区三区在线观看| 一本大道久久a久久精品| av在线播放免费不卡| 亚洲精品国产一区二区精华液| 婷婷六月久久综合丁香| 免费看a级黄色片| 欧美黑人巨大hd| 亚洲欧美激情综合另类| 日本在线视频免费播放| 日韩免费av在线播放| 国产精品1区2区在线观看.| 亚洲av成人av| 亚洲精品久久国产高清桃花| 非洲黑人性xxxx精品又粗又长| 婷婷精品国产亚洲av| 久久婷婷人人爽人人干人人爱| 久99久视频精品免费| 男男h啪啪无遮挡| 亚洲激情在线av| 亚洲成av人片免费观看| 精品久久久久久久久久久久久| 一级黄色大片毛片| 国产av一区二区精品久久| aaaaa片日本免费| 在线观看舔阴道视频| 国产免费av片在线观看野外av| 好男人在线观看高清免费视频| 成人高潮视频无遮挡免费网站| 男女下面进入的视频免费午夜| 在线观看一区二区三区| 黑人操中国人逼视频| 精品久久久久久久人妻蜜臀av| 欧美黄色淫秽网站| 午夜久久久久精精品| 欧美日韩亚洲国产一区二区在线观看| 国产免费男女视频| 午夜免费观看网址| 欧美成人一区二区免费高清观看 | 夜夜夜夜夜久久久久| 精品久久久久久成人av| 特级一级黄色大片| 国产精品影院久久| 国产精品av久久久久免费| 淫妇啪啪啪对白视频| 99国产极品粉嫩在线观看| 亚洲欧美一区二区三区黑人| 熟女少妇亚洲综合色aaa.| 国产伦一二天堂av在线观看| 国产男靠女视频免费网站| 亚洲九九香蕉| 久久久国产成人精品二区| 免费在线观看视频国产中文字幕亚洲| 国产欧美日韩一区二区三| 亚洲国产欧美一区二区综合| 精品一区二区三区av网在线观看| 国产一区二区在线观看日韩 | 搡老岳熟女国产| cao死你这个sao货| 一级作爱视频免费观看| 最新在线观看一区二区三区| 亚洲 欧美 日韩 在线 免费| 麻豆国产97在线/欧美 | 老司机福利观看| 亚洲av五月六月丁香网| 麻豆国产97在线/欧美 | 国产精品亚洲av一区麻豆| 久久午夜亚洲精品久久| 极品教师在线免费播放| 日日夜夜操网爽| 欧美性猛交黑人性爽| 久久久久国产一级毛片高清牌| 国产精品av视频在线免费观看| 99久久精品国产亚洲精品| 亚洲真实伦在线观看| 久久这里只有精品19| 亚洲 欧美 日韩 在线 免费| 99久久国产精品久久久| 日韩欧美国产一区二区入口| 好男人在线观看高清免费视频| 97碰自拍视频| 欧美日韩一级在线毛片| 日韩免费av在线播放| 两性夫妻黄色片| 身体一侧抽搐| 18禁美女被吸乳视频| 三级男女做爰猛烈吃奶摸视频| 高清毛片免费观看视频网站| 美女 人体艺术 gogo| 欧美国产日韩亚洲一区| 国产一区二区在线观看日韩 | 欧美丝袜亚洲另类 | 成人国语在线视频| 中文字幕高清在线视频| av国产免费在线观看| 亚洲七黄色美女视频| 国产精品亚洲av一区麻豆| 午夜视频精品福利| 美女高潮喷水抽搐中文字幕| 国产v大片淫在线免费观看| 欧美绝顶高潮抽搐喷水| 国产av一区二区精品久久| 欧美成人一区二区免费高清观看 | 我的老师免费观看完整版| 777久久人妻少妇嫩草av网站| 一级黄色大片毛片| 欧美黄色片欧美黄色片| 亚洲色图 男人天堂 中文字幕| 欧美乱码精品一区二区三区| 琪琪午夜伦伦电影理论片6080| av片东京热男人的天堂| 韩国av一区二区三区四区| 亚洲熟妇熟女久久| 亚洲欧美日韩高清专用| 欧美中文日本在线观看视频| 欧美不卡视频在线免费观看 | 成人亚洲精品av一区二区| 美女免费视频网站| 国产精品自产拍在线观看55亚洲| 免费看日本二区| 精品无人区乱码1区二区| 夜夜夜夜夜久久久久| 亚洲男人的天堂狠狠| 久99久视频精品免费| 成年女人毛片免费观看观看9| 国产精品99久久99久久久不卡| 亚洲精品粉嫩美女一区| 国产成人aa在线观看| 国产成人啪精品午夜网站| 亚洲熟女毛片儿| 国产亚洲av嫩草精品影院| 天天一区二区日本电影三级| 性色av乱码一区二区三区2| 亚洲 欧美一区二区三区| 一a级毛片在线观看| 一进一出抽搐动态| 国产精品综合久久久久久久免费| 亚洲av成人av| 日韩大码丰满熟妇| 国产成+人综合+亚洲专区| 精华霜和精华液先用哪个| 男插女下体视频免费在线播放| 国产精品一区二区三区四区免费观看 | 在线观看66精品国产| 99国产极品粉嫩在线观看| 亚洲av电影在线进入| 国产成人av激情在线播放| 国产精品影院久久| 我要搜黄色片| 人人妻人人看人人澡| 久久这里只有精品中国| 一级作爱视频免费观看| 身体一侧抽搐| 俄罗斯特黄特色一大片| 午夜福利成人在线免费观看| 亚洲国产精品999在线| 国产久久久一区二区三区| 午夜福利欧美成人| 亚洲欧美日韩高清在线视频| 一夜夜www| 特级一级黄色大片| 香蕉国产在线看| 精品福利观看| 美女 人体艺术 gogo| 两个人免费观看高清视频| 国产精品永久免费网站| 琪琪午夜伦伦电影理论片6080| 国产精品电影一区二区三区| 欧美在线一区亚洲| 日本免费一区二区三区高清不卡| 男人的好看免费观看在线视频 | 美女大奶头视频| 亚洲欧洲精品一区二区精品久久久| 国产一区在线观看成人免费| 窝窝影院91人妻| 黄片小视频在线播放| 欧美日本视频| 亚洲国产欧美一区二区综合| 国产精品久久久久久久电影 | 波多野结衣高清作品| 亚洲欧洲精品一区二区精品久久久| 香蕉av资源在线| 成人18禁高潮啪啪吃奶动态图| 草草在线视频免费看| 国产成人精品久久二区二区免费| 久久亚洲真实| 麻豆成人av在线观看| 日本撒尿小便嘘嘘汇集6| 一进一出好大好爽视频| 精品国产乱子伦一区二区三区| 少妇裸体淫交视频免费看高清 | 搞女人的毛片| 中亚洲国语对白在线视频| 午夜福利高清视频| 高清毛片免费观看视频网站| 少妇人妻一区二区三区视频| 国产日本99.免费观看| 亚洲,欧美精品.| 两性午夜刺激爽爽歪歪视频在线观看 | 热99re8久久精品国产| 国产精品久久久人人做人人爽| 狂野欧美激情性xxxx| 国产欧美日韩精品亚洲av| 观看免费一级毛片| 亚洲无线在线观看| 日本成人三级电影网站| 首页视频小说图片口味搜索| 国产在线观看jvid| 丁香六月欧美| 黄片小视频在线播放| 在线观看舔阴道视频| 欧美成狂野欧美在线观看| 欧美高清成人免费视频www| 丝袜美腿诱惑在线| 最近最新中文字幕大全电影3| 亚洲精品美女久久av网站| tocl精华| 97碰自拍视频| 嫩草影视91久久| 男女下面进入的视频免费午夜| 国内久久婷婷六月综合欲色啪| 又粗又爽又猛毛片免费看| 久99久视频精品免费| 三级男女做爰猛烈吃奶摸视频| 黄片大片在线免费观看| 老司机深夜福利视频在线观看| 成在线人永久免费视频| 国产在线精品亚洲第一网站| 国产精品日韩av在线免费观看| svipshipincom国产片| 免费在线观看完整版高清| 欧美中文日本在线观看视频| 欧美成人午夜精品| 久久精品aⅴ一区二区三区四区| 久久久久九九精品影院| 国产亚洲精品久久久久久毛片| 最近最新中文字幕大全免费视频| 国产成人精品无人区| 国产一区二区三区在线臀色熟女| 午夜成年电影在线免费观看| 成人国产一区最新在线观看| e午夜精品久久久久久久| 亚洲人成网站在线播放欧美日韩| 国产熟女午夜一区二区三区| 好看av亚洲va欧美ⅴa在|