Langmuir adsorptionTo illustrate the difference in choices of ensembles.
Canonical ensembleFind the partition function from the number of ways to distribute
\Omega(N)=\frac{M!}{N!(M-N)!}\\
\implies Q=\frac{M!}{N!(M-N)!}\exp(\beta N\epsilon)With Stirling’s approximation, chemical potential can be...
Fundamental ideaThink about thermodynamicsThe observable properties of systems containing very large numbers of particles depend only on specifying a few macroscopic properties - internal energy, temperature, volume, pressure, density, etc.
Most experiments measure averaged properties - over many...
Rigorous maths is not essential for the sake of this course, so that will only be added later if required.
DiffractionGeometry
Symbol
Meaning
\mathbf{r}
Position
\mathbf{s_0}
Unit vector of incident beam
\mathbf{s}
Unit vector of diffracted beam
\mathbf{S=(s-s_0)}/\lambda
Scattering ...
It should be obvious but 主题是针对英国。如果没有了解政府进入Stage II的措施以及理由，在最后附了摘要。（Credit: LZH）
为什么不在质疑一个人“为什么不”之前，如果你没有站在他的立场上思考一下为什么不，那这个质疑是极不负责任的。
一场瘟疫面前，政府为什么不轻举妄动的理由很多，大家也都能慢慢看到了。最近的例子，美国一封闭欧洲的航班，DJI就暴跌10%。这说明从经济上看，任何的封闭性措施，至少在大多数人（资本）看来，在短期内都会对经济造成更加负面的、极其严重的影响。
同样的，在其他方面，任何措施对国家、社会的影响都不可小觑。多少小企业就此破产、多少投资...
Cambridge Part II B7 course.
RepresentationsThe representation matrix of an operation is defined with a left contraction
\hat{R}\phi_i=\sum_j \phi_j D_{ji}(R).Great Orthogonality TheoremIf \Gamma_a and \Gamma_b are two irreducible unitary representations, then their representation matrices satis...
Key equations for Cambridge Part II Theoretical techniques course.
A brief note on the use of enolates in syntheses.
Enolate alkylationCondition overviewBy electrophile
Electrophile type
Conditions
Note
Activated R-X
Best with enamines1. \ce{R2NH},\ \rm{cat\ }\ce{H+}2. \ce{R-X}3. \ce{H+}
Tertiary R-X
Lewis acid to form cation\ce{TiCl4}, TMS enol ether ...
Updated to electronic spectroscopies.
Interaction of molecules with radiation
n
i
n
j
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Three types of interactions
Absorption
Stimulated emission
Spontaneous ...
Essential Thermodynamics - summary of Cambridge IA chemistry TD course.
Laws
First Law:
dU =\delta q+ \delta w \label{td1}\tag{1}
Second Law: entropy of the Universe increases in a spontaneous process.
Entropy is classically defined as
dS=\frac{\delta q_{rev}}{T}. \tag{2}\label{entropy} ...
让对滑雪完全无感的我，回到全法最大滑雪度假村Val Thoren的唯一动力。The motivation for a ski-phobia like me to return to Val Thoren.
参与牛剑Varsity trip前往法国享受的一次滑雪之旅已经过去半年多了，而这家餐厅的记忆也自然而然随时间开始淡去。
“不行，不能忘，必须记录下来！”它给我带来的体验就是有这么优越。
于是，在这不尴不尬的时间点，胡编了一个“之最”的名号来赞美它。不想说得太绝对，毕竟我也没去过足够多的优秀餐厅。“学年最佳”，就一点也不假，完全可以甩心中的第二名13条街。
在短短的一周时间中，我们就...
