麦克斯韦妖悖论说明了什么？
What does Maxwell's demon paradox illustrate?
麦克斯韦设想一个小妖通过开闭闸门为快慢分子分类来降低熵，看似违背第二定律。Bennett 在 1982 年指出，妖要记录并擦除信息本身就会产生熵增，因此整体仍满足熵不减。
Maxwell imagined a demon sorting fast and slow molecules to lower entropy, seemingly violating the second law. Bennett argued in 1982 that the demon's measurement and erasure of information itself generates entropy, so the total still respects the law.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-04
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麦克斯韦 1867 年书信；Bennett,《The thermodynamics of computation—a review》,International Journal of Theoretical Physics,1982 (DOI: 10.1007/bf02084158)
Maxwell (1867 letter); Bennett, 'The thermodynamics of computation—a review', International Journal of Theoretical Physics, 1982, DOI: 10.1007/bf02084158
独立核验依据 · Independent verification: 核验依据 1 Crossref DOI 10.1007/bf02084158
#麦克斯韦妖 #信息熵 #热力学第二定律
熵与“时间之箭”之间是什么关系？
What is the relation between entropy and the 'arrow of time'?
宏观过程的不可逆性由熵增原理刻画：孤立系统的熵永不减少，这给热力学时间赋予单一方向。玻尔兹曼用分子微观状态数解释熵，把“未来”定义为熵更高的方向。
The irreversibility of macroscopic processes is captured by the increase of entropy: an isolated system's entropy never decreases, giving thermodynamic time a single direction. Boltzmann linked entropy to the number of microstates, defining the 'future' as the direction of higher entropy.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-04
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玻尔兹曼《气体理论讲义》1896；Feynman《物理学讲义》第一卷
Boltzmann, Lectures on Gas Theory (1896); Feynman, The Feynman Lectures on Physics (Vol. I)
独立核验依据 · Independent verification: 核验依据 1 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#熵 #时间之箭 #热力学第二定律
玻尔兹曼分布描述了粒子在什么状态下如何分配能量？
How does the Boltzmann distribution describe how particles share energy?
在热平衡下，处于能量为 E 的某个状态的粒子数，正比于 e^(−E/kT)——能量越高越稀有，温度越高高能态越容易被占据。这把微观粒子的概率与宏观温度联系起来，是气体速率分布、化学反应速率（阿伦尼乌斯）、乃至恒星中核反应率的基础。麦克斯韦–玻尔兹曼分布是其最常见的具体形式。
At thermal equilibrium the number of particles in a state of energy E is proportional to e^(−E/kT): higher energy is rarer, and higher temperature populates high-energy states more. This ties microscopic probabilities to macroscopic temperature and underlies gas speed distributions, reaction rates (Arrhenius), and even stellar nuclear rates. The Maxwell–Boltzmann distribution is its most familiar form.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
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R. K. 帕斯里亚《统计力学》第2章；麦克斯韦与玻尔兹曼 19 世纪气体动理论
R. K. Pathria, 'Statistical Mechanics', Ch. 2; Maxwell & Boltzmann, 19th-c. kinetic theory of gases
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL1624664W：Statistical mechanics（首
#玻尔兹曼分布 #统计力学 #热平衡
为什么温度不能真正降到「绝对零度」（−273.15°C）？
Why can temperature never actually reach absolute zero (−273.15 °C)?
热力学第三定律指出，靠有限步骤不可能把一个系统的熵降到零，因此绝对零度不可达到，只能无限逼近。量子力学也说明即使在零温附近，粒子仍有「零点能」无法被取走。实验上物理学家用激光冷却与蒸发冷却把原子降到纳开尔文量级，却始终留有一丝残余运动。
The third law of thermodynamics says no finite sequence of operations can reduce a system's entropy to zero, so absolute zero is unreachable—only approachable. Quantum mechanics adds that particles retain 'zero-point energy' even near zero temperature. Experiments using laser and evaporative cooling reach nanokelvin scales yet always leave residual motion.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
秦允豪,《热学》,高等教育出版社,2011
Qin Yunhao, Thermal Physics, Higher Education Press, 2011
#绝对零度 #热力学第三定律 #零点能
布朗运动如何帮助人们测得阿伏伽德罗常数？
How did Brownian motion help determine Avogadro's number?
爱因斯坦在 1905 年用统计物理预言悬浮微粒的随机位移与温度和黏度相关，Perrin 于 1908 年通过实验计数证实并由此算出阿伏伽德罗常数，成为原子真实存在的关键证据。
Einstein's 1905 statistical theory predicted that the random jiggle of suspended particles depends on temperature and viscosity; Perrin's 1908 counts confirmed it and yielded Avogadro's number, providing key evidence that atoms are real.
难度 进阶 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
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出处备注：著录含书名，但缺版次 / 出版社 / 年份中的一部分，需编辑补全后才能做独立比对。
爱因斯坦 1905 年论文；Perrin《原子》1913
Einstein (1905 Brownian motion paper); Perrin, Les Atomes (1913)
#布朗运动 #阿伏伽德罗常数 #统计物理
为什么热机效率永远达不到 100%？
Why can a heat engine never be 100% efficient?
卡诺定理指出，任何循环热机必须把一部分热量排给低温热源，其效率上限由两热源的温度之比（η=1−T冷/T热）决定。要把热量全部转为功而不排热，就违背了开尔文表述的第二定律。
Carnot's theorem states that any cyclic heat engine must reject some heat to a colder reservoir, with the maximum efficiency set by the temperature ratio. Converting all heat to work without rejection would violate the Kelvin statement of the second law.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-03
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卡诺《论火的动力》1824；Callen《热力学与统计物理》
Carnot, Reflections on the Motive Power of Fire (1824); Callen, Thermodynamics and an Introduction to Thermostatistics
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL10501410W：Reflections on the mot
#卡诺定理 #热机效率 #热力学第二定律
相变时为什么会吸收或释放潜热？
Why is latent heat absorbed or released during a phase change?
在熔点或沸点，加入的热量用于改变分子间结合方式（破坏有序结构）而不是升高温度，这部分能量称为潜热。冰在 0°C 熔化时吸收的热量全部用于打破氢键网络。
At a melting or boiling point the added heat goes into rearranging intermolecular bonds rather than raising temperature, and that energy is the latent heat. Ice at 0°C uses all absorbed heat to break its hydrogen-bond network instead of warming up.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-03
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朗道与栗弗席兹《统计物理学》；Ehrenfest 相变分类
Landau & Lifshitz, Statistical Physics; Ehrenfest classification of phase transitions
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787040305722（豆瓣书目条目: 统计物理学）；本条出处含多部著作，此标识只担保上面点名的这
#潜热 #相变 #熔化
热力学第一定律说能量既不能凭空产生也不能凭空消失，怎么表述？
How is the first law of thermodynamics stated in terms of energy conservation?
它说系统内能的变化等于吸收的热量减去对外做的功（ΔU=Q−W）。能量只会从一种形式转为另一种，总量不变。
It states that the change in a system's internal energy equals heat absorbed minus work done (ΔU=Q−W). Energy only changes form; the total amount is conserved.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
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《费曼物理学讲义》
The Feynman Lectures on Physics
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#能量守恒 #内能 #热力学第一定律
为什么冰融化时温度一直停在 0℃，却还在吸热？
Why does melting ice stay at 0°C while still absorbing heat?
冰在融化时要先打破晶体里的氢键，这部分热量用于改变物态而非升温，叫熔化潜热。直到全部变成水，温度才继续上升。
Melting ice must first break the hydrogen bonds in its crystal; that heat changes the state rather than raising temperature, called the latent heat of fusion. Only after all ice turns to water does the temperature climb.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 来源待核验 · Source pending review
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出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
Enrico Fermi 著《Thermodynamics》（热力学）
Enrico Fermi, Thermodynamics
#潜热 #相变 #熔化
黑体辐射和“红得发烫”的现象有什么关系？
How is blackbody radiation related to things glowing red hot?
物体受热会发出热辐射，温度越高峰值波长越短。约 500℃ 时发红光，更高时转黄白；普朗克公式正是描述这种光谱的开端。
Heated objects emit thermal radiation whose peak wavelength shortens with temperature. Around 500°C they glow red, hotter ones yellow-white; Planck's law describes this spectrum.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-08-23
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秦允豪,《热学》,高等教育出版社,2011
Qin Yunhao, Thermal Physics, Higher Education Press, 2011
#黑体辐射 #热辐射 #普朗克
热力学第二定律和「熵」到底在说什么？
What do the second law of thermodynamics and 'entropy' really say?
第二定律说，一个孤立系统的熵（可理解为「混乱度」或不可用能的度量）永不减少，只会增大或保持不变。它解释了为什么热量自发从热处流向冷处、为何打碎的杯子不会自己复原——方向性来自大量微观状态数的统计。玻尔兹曼用 S = k ln W 把熵与微观可能状态数联系起来。
The second law says the entropy of an isolated system—roughly its disorder or unavailable energy—never decreases, only grows or stays constant. It explains why heat flows from hot to cold and why a broken cup won't reassemble: directionality comes from counting microscopic states. Boltzmann linked entropy to those states via S = k ln W.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 来源待核验 · Source pending review
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出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
《热力学与统计物理》（汪志诚）熵与玻尔兹曼关系章节；玻尔兹曼 1877 年统计诠释
Wang Zhicheng, 'Thermodynamics and Statistical Physics', on entropy and Boltzmann's relation; Boltzmann (1877)
#热力学第二定律 #熵 #不可逆性
什么是「相变」和「临界现象」，为什么水结冰和磁铁消磁是同一类问题？
What are 'phase transitions' and 'critical phenomena,' and why are freezing water and a demagnetizing magnet the same kind of problem?
相变是物质宏观性质在某一条件下发生突变（如水在0°C结冰、铁在居里温度失去磁性），系统的对称性与关联长度随之改变。临界现象关注相变点附近物理量按幂律发散的行为；昂萨格1944年精确解出二维伊辛模型，开启了现代临界现象理论。它们之所以同类，是因为都可用「序参量」和对称性破缺统一描述。
A phase transition is a sudden macroscopic change at a threshold (water freezing at 0 °C, iron losing magnetism at its Curie temperature), with symmetry and correlation length changing. Critical phenomena study power-law divergences near that point; Onsager's exact 1944 solution of the 2D Ising model launched modern theory. They are the same class because an 'order parameter' and symmetry breaking describe them all.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-11-04
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昂萨格（L. Onsager）,《Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition》,Physical Review,1944 (DOI: 10.1103/physrev.65.117)；美国物理学会《现代物理评论》相变综述
L. Onsager, 'Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition', Physical Review, 1944, DOI: 10.1103/physrev.65.117; APS 'Reviews of Modern Physics' on phase transitions
独立核验依据 · Independent verification: 核验依据 1 Crossref DOI 10.1103/physrev.65.117
#相变 #临界现象 #序参量
水烧开时冒出的“白气”是水蒸气吗？
Is the white steam from boiling water actually water vapor?
看不见的水蒸气是无色气体，离开水面遇冷才凝结成无数小水滴，那团“白气”其实是小水珠。真正的水蒸气你是看不见的。
Invisible water vapor is a colorless gas; only after it leaves the water and cools does it condense into tiny droplets. That white puff is actually little water drops, not vapor itself.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
Enrico Fermi 著《Thermodynamics》（热力学）
Enrico Fermi, Thermodynamics
#沸腾 #水蒸气 #凝结
为什么「永动机」在物理上不可能实现？
Why is a 'perpetual motion machine' impossible in physics?
第一类永动机想不消耗能量却不断做功，违背能量守恒（热力学第一定律）；第二类想从单一热源不断取热做功，违背第二定律（熵增）。实际机器还有摩擦等耗散，能量只会越来越少。因此各国专利局（如美国专利商标局）通常直接驳回永动机申请，要求先证明不违反热力学定律。
A first-kind machine that does work without energy input violates conservation of energy (the first law); a second-kind one that extracts work from a single heat reservoir violates the second law (entropy increase). Real machines also lose energy to friction. Patent offices such as the USPTO routinely reject perpetual-motion claims unless they first show no thermodynamic law is broken.
难度 入门 · 适合 大众
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：此条未指向带版次的可引用著作（通识性内容、机构文件或未展开的英文书名），本库不提供独立书目出处；如需精确引用，需由编辑补全具体篇目与版次。
美国专利商标局（USPTO）对「永动机」类申请的审查指南（要求先证明不违反热力学定律）
U.S. Patent and Trademark Office (USPTO) examining guidelines rejecting perpetual-motion applications absent proof of thermodynamic compliance
#永动机 #能量守恒 #热力学定律
为什么铁轨之间要留缝隙？
Why are gaps left between railway tracks?
金属受热会膨胀、变长，留缝让铁轨夏天有伸长的余地，避免相互顶弯或拱起。这是热胀冷缩在工程中必须考虑的例子。
Metal expands and lengthens when heated; the gaps give tracks room to grow in summer so they don't buckle or lift. It's a practical case of thermal expansion.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
秦允豪,《热学》,高等教育出版社,2011
Qin Yunhao, Thermal Physics, Higher Education Press, 2011
#热胀冷缩 #膨胀 #工程
同样温度下，为什么金属勺摸起来比木勺凉？
Why does a metal spoon feel colder than a wooden one at the same temperature?
金属导热系数远高于木材，会更快把手指的热量带走，使皮肤温度下降更明显，于是感觉更凉。体感温度反映的是热流速率而非物体本身温度。
Metal has a far higher thermal conductivity than wood, so it draws heat from your finger much faster and cools the skin more noticeably, feeling colder. What you sense is the rate of heat flow, not the object's actual temperature.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
Incropera《传热与传质基础》；傅里叶热传导定律
Incropera, Fundamentals of Heat and Mass Transfer; Fourier's law of heat conduction
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL2975219W：Fundamentals of heat an
#热导率 #触感温度 #热传导