约瑟夫·斯特凡Josef Stefan

约瑟夫·斯特凡的父母虽然住在奥匈帝国（今奥地利）克拉根福附近，却是斯洛文尼亚裔，讲斯洛文尼亚语。他的父亲Ales 斯特凡（1805-1872）是磨坊主和面包师。斯特凡的母亲Marija Startinik（1815-1863）受雇为女仆。他们两人都不识字，也没有结婚。斯特凡在克拉根福上小学时就显露出才华，他表现出既有愿望又有能力在老师推荐的文理中学中取得好成绩。然而，作为一个私生子，他不被允许上文理中学，所以当他十一岁时，他的父母结了婚，给斯特凡接受良好教育的机会。斯特凡于1846年进入克拉根福的文理中学。

1848年3月13日，即斯特凡十三岁生日前十一日，奥地利爆发了一场革命。这场革命是由同年二月的巴黎革命引发的。人们寻求基本自由，但国家分裂，革命和反革命团体争夺权力。斯特凡正处于易受影响的年龄，革命使他更加意识到各种族群和他自己的斯洛文尼亚血统。他的反应是写斯洛文尼亚诗歌并发表。他的诗歌涉及科学主题，有时激烈爱国，有时则浪漫。1853年，他作为班上顶尖学生完成了文理中学的学业，尽管他有多种兴趣可以在大学学习，但他相当确定数学和物理适合他。他曾考虑加入本笃会一段时间，但很快放弃了这一想法。

斯特凡于1853年进入维也纳大学。四年后，他毕业并获得数学和物理学位。在整个学生时代，他继续写斯洛文尼亚诗歌和散文，但在受到斯洛文尼亚文学专家的批评后，他在从维也纳大学毕业前后放弃了这一爱好。接下来的一年，他为药学学生教授物理，然后接受了卡尔·路德维希在维也纳大学生理研究所的职位。在这里，他进行了水通过管道流动的实验工作。在此期间，他准备habilitate，并于1858年完成。1858年被任命为维也纳大学数学物理讲师，1860年当选为奥地利科学院会士，1863年成为维也纳大学教授。1866年，他成为维也纳物理研究所所长。该研究所由克里斯蒂安·多普勒于1850年创立。

他在维也纳大学的职业生涯包括在1869-70年担任哲学学院院长，并在1876-77年担任校长。我们注意到他在1860年当选为奥地利科学院。他于1865年成为正式成员，从1875年起担任科学院数学科学部的秘书，并从1885年起担任科学院副院长，直到去世。

斯特凡开始的研究计划范围广泛，涉及多个不同领域。他非常钦佩詹姆斯·克拉克·麦克斯韦的贡献，并在使他的工作在欧洲大陆为人所知方面发挥了重要作用。正是在詹姆斯·克拉克·麦克斯韦的论文中，他看到了以下内容：-

几乎不可能通过直接实验来确定气体的电导率值，因为从容器侧面辐射的热量将远远大于通过空气传导的热量，即使可以完全阻止电流。

当然，詹姆斯·克拉克·麦克斯韦关于困难的看法是正确的，但斯特凡是一个迎接挑战的人，尤其是在设计被认为几乎不可能的实验中。斯特凡推理说，需要一种新仪器来确定空气的热导率，于是他着手设计了一种他称之为透热计的仪器，并在他的论文Untersuchung über die Wärmeleitung in Gasen, Erste AbhandlungⓉ（爱德华·斯图迪论气体中的热传导，第一论）(1872)中进行了描述。有了这个，他能够找到空气热导率的值，误差仅约为10%。詹姆斯·克拉克·麦克斯韦，以及同样研究过这个问题的鲁道夫·克劳修斯，已经推断出热导率应该与气体的压力无关，而斯特凡能够通过实验验证这一点。他接着找到了氢、一氧化二氮、甲烷、一氧化碳和二氧化碳的热导率，并在Untersuchung über die Wärmeleitung in Gasen, Zweite AbhandlungⓉ（斯图迪论气体中的热传导，第二论）(1875)中展示了结果。

斯特凡在1879年通过经验表明，黑体的总辐射与其绝对温度的四次方成正比。这是他最著名的结果，正是我们上面描述的工作使他能够进行下一项研究。事实上，他是通过廷德尔在1865年一本书中产生的数据得出这个结果的。廷德尔测量了由电流加热的铂丝的辐射。斯特凡使用廷德尔的数据，在Über die Beziehung zwischen der Wärmestrahlung und der TemperaturⓉ（论热辐射与温度的关系）(1879)中写道：-

从微弱的红热（约525°C）到完全白热（约1200°C），辐射强度从10.4增加到122，因此几乎增加了十二倍（更精确地说是11.7倍）。这一观察使我取热辐射与绝对温度的四次方成正比。绝对温度273 + 1200和273 + 525的四次方之比给出11.6。

斯特凡随后用它确定了太阳表面的近似温度。路德维希·玻尔兹曼是斯特凡的学生之一，他在1884年证明了这个斯特凡-路德维希·玻尔兹曼定律可以用数学方法加以论证。

在这项工作之后，斯特凡研究了极地冰盖问题。几艘船试图寻找西北航道，并在这样做时在冬季被困在极地冰中。船上的科学家记录了空气温度和冰的生长。斯特凡意识到这是他一直在研究的问题的一个变体。这个问题涉及热量跨越移动边界的传递，而不是跨越固定边界的传递。他在Über die Theorie der Eisbildung, insbesondere über die Eisbildung im Polarmeere Ⓣ（论冰的形成理论，特别是极地海洋中的冰）(1889)中展示了他的结果。

斯特凡的其他工作包括表面张力和蒸发的研究，在此期间他提出了今天所谓的‘斯特凡数’和‘斯特凡定律’。他还进行了交流电的研究，研究线圈的感应系数。他广泛的主题范围可以通过指出他还对光学做出了重要贡献来说明，在艾萨克·牛顿的实验中发现了次级环。

斯特凡的一生完全献给了科学。他常常睡在实验室里，有时会在实验室里一连待上好几天而不出来。当然，如此全身心地投入工作，斯特凡几乎没有时间结交朋友，也几乎没有什么社交生活。然而，他受到学生们的喜爱，他们觉得他是一位出色的教师，能够激发他们对物理学的热情。尽管他作为研究者的最大长处在于实验方面，但他同时也是一位杰出的数学家，在理论方面也能展现出洞察力。他最著名的学生路德维希·玻尔兹曼这样评价他（例如见[5]）：——

他运用高等数学的工具，并且懂得如何把最艰深的发展以最清晰、最明白的形式呈现出来，而无需诉诸数学形式主义。……[他]从不试图炫耀[自己的]智力优越。[他]令人振奋的幽默把最困难的讨论变成学生的一场有趣游戏，这给我留下了极其深刻的印象。

路德维希·玻尔兹曼描绘了一幅美妙的研究环境的图景：——

没有什么能减损[斯特凡]品格的卓越，[他]对年轻学者施展的魔力。那种魔力只能亲身感受。[这种体验]作为严肃而富有灵感的实验活动的象征，伴随了我一生。

斯特凡一生中大部分时间未婚，他太专注于自己的职业，没有空间留给妻子或家庭。然而，1891年，当他56岁时，他娶了寡妇Marija Neumann。婚后他只活了一年多一点，便因中风去世。他被安葬在维也纳的中央公墓。

Both Josef Stefan's parents, although living near Klagenfurt in Austria-Hungary (now Austria), were of Slovenian origin and spoke Slovenian. His father, Ales Stefan (1805-1872), worked as a miller of flour and as a baker. Josef's mother, Marija Startinik (1815-1863), was employed as a maidservant. They were both illiterate and were not married. Josef showed his brilliance when at elementary school in Klagenfurt and he showed himself to have both the desire and ability to do well at the Gymnasium which was recommended by his teachers. However, as an illegitimate child he would not be allowed to attend a Gymnasium so, when he was eleven years old, his parents married to give Josef to opportunity of a good education. Stefan entered the Gymnasium in Klagenfurt in 1846.

On 13 March 1848, eleven days before Stefan's thirteenth birthday, a Revolution began in Austria. It was prompted by the Paris Revolution in February of the same year. People sought basic freedoms but the country was divided and revolutionary and counter-revolutionary groups fought for power. Stefan was at an impressionable age and the Revolution made him much more aware of the various ethnic groupings and his own Slovenian origins. He reacted by writing Slovenian poetry which he published. His poetry touched on scientific topics as well as sometime being fiercely patriotic while at other times it was romantic. In 1853 he completed his studies at the Gymnasium as the top student in his class and, although having a range of interests which he could have chosen to study at university, nevertheless was quite certain that mathematics and physics were for him. He did consider joining the Benedictine Order for a while but soon gave up the idea.

Stefan entered the University of Vienna in 1853. He graduated four years later with a degree in mathematics and physics. He continued to write Slovenian poetry and prose throughout his student years but after criticisms by the Slovenian literary experts, he gave this up around the time he graduated from the University of Vienna. For the next year he taught physics for pharmacy students, then accepted a position with Karl Ludwig at the Physiology Institute of Vienna University. Here he carried out experimental work on the flow of water through tubes. During this period he was preparing to habilitate which he did in 1858. Appointed a lecturer in mathematical physics at the University of Vienna in 1858, he was elected to the Austrian Academy of Sciences in 1860, then he became a professor at the University of Vienna in 1863. In 1866 he became director of the Physical Institute at Vienna. This Institute had been founded by Doppler in 1850.

His career at the University of Vienna included a spell as dean of the Philosophy Faculty in 1869-70, and rector in 1876-77. We noted his election to the Austrian Academy of Sciences in 1860. He became a full member in 1865, was secretary of the Mathematical Sciences Class of the Academy from 1875, and was vice-president of the Academy from 1885 until his death.

The programme of research that Stefan embarked on was wide ranging across a number of different areas. He was a great admirer of Maxwell's contributions and was a major player in making his work known on the Continent. It was in Maxwell's papers that he came across the following:-

It would be almost impossible to establish the value of the conductivity of a gas by direct experiment, as the heat radiated from the sides of the vessel would be far greater than the heat conducted through the air, even if current could be entirely prevented.

Of course Maxwell was right about the difficulties but Stefan was one to rise to a challenge, especially when it came to devising experiments thought to be almost impossible. A new instrument would be needed to determine the thermal conductivity of air, reasoned Stefan, and he set about devising one which he called a diathermometer described in his paper Untersuchung über die Wärmeleitung in Gasen, Erste Abhandlung Ⓣ (1872). With this he was able to find a value of the thermal conductivity or air which only has an error of about 10%. Maxwell, and also Clausius who had also worked on the problem, had deduced that thermal conductivity should be independent of the pressure of the gas, and Stefan was able to verify this experimentally. He went on the find the thermal conductivity of hydrogen, nitrous oxide, methane, carbon monoxide, and carbon dioxide, presenting the results in Untersuchung über die Wärmeleitung in Gasen, Zweite Abhandlung Ⓣ (1875).

Stefan showed empirically, in 1879, that total radiation from a blackbody is proportional to the fourth power of its absolute temperature. This is the result for which he is best known and it was the work which we have described above which set him up to undertake this next piece of research. In fact he was led to the result by data produced by Tyndall in an 1865 book. Tyndall measured the radiation from a platinum wire heated by an electric current. Stefan, using Tyndall's data, wrote in Über die Beziehung zwischen der Wärmestrahlung und der Temperatur Ⓣ (1879):-

From weak red heat (about 525° C) to complete white heat (about 1200° C) the intensity of radiation increases from 10.4 to 122, thus nearly twelvefold (more precisely 11.7). This observation caused me to take the heat radiation as proportional to the fourth power of the absolute temperature. The ratio of the absolute temperature 273 + 1200 and 273 + 525 raised to the fourth power gives 11.6.

Stefan then applied it to determine the approximate temperature of the surface of the Sun. Boltzmann, who was one of Stefan's students, showed in 1884 that this Stefan-Boltzmann law could be demonstrated mathematically.

After this work, Stefan looked at the problem of the polar ice caps. Several ships had been trying to find the Northwest Passage and in so doing had become stuck in the polar ice over the winter. The scientists on board had taken recordings of the air temperature and ice growth. Stefan realised that this was a variant of the problem he had been studying. Instead of considering the transfer of heat across a fixed boundary, this problem involved the transfer of heat across a moving boundary. He presented his results in Über die Theorie der Eisbildung, insbesondere über die Eisbildung im Polarmeere Ⓣ (1889).

Other work by Stefan includes studies of surface tension and evaporation, during which he proposed what today is called 'Stefan's number' and 'Stefan's law'. He also undertook research on alternating electric currents, studying the induction coefficients of wire coils. His wide range of topics can be illustrated by noting that he also made important contributions to optics, discovering secondary rings in Newton's experiments.

The life which Stefan led was totally dedicated to science. He frequently slept in his laboratory and on occasions would spend several days in the laboratory without ever leaving. Of course with such total dedication to his work, Stefan had little time for friends and had hardly any social life. However he was liked by his students who found him an excellent teacher who could enthuse them for physics. Although his great strength as a researcher was on the experimental side, nevertheless he was an excellent mathematician who could show insight on the theoretical side too. His most famous student, Boltzmann said this of him (see for example [5]):-

He used the tools of advanced mathematics and understood how to present the most difficult developments in the clearest and most lucid form without ever having to resort to mathematical formalism. ... [He] never tried to flaunt [his] mental superiority. [His] uplifting humour, which turned the most difficult discussion into an entertaining game for the student, made such a deep impression on me.

Boltzmann painted a picture of a wonderful research environment:-

Nothing diminishes the excellence of [Stefan's] character, the magic [he] worked on the young academics. That magic could only be experienced personally. [The experience] stayed with me my whole life as a symbol of serious, inspired experimental activity.

For most of his life Stefan was unmarried, too dedicated to his profession to have space for wife or family. However, in 1891 when he was 56 years old, he married Marija Neumann who was a widow. He lived only a little over a year after his marriage, suffering a stroke. He was buried in the Zentralfriedhof in Vienna.