[別館]球面倶楽部零八式markIISR

東大入試数学中心。解説なので解答としては不十分。出題年度で並ぶようにしている。大人の解法やうまい解法は極めて主観的に決めている。

1916年(大正5年)東京帝國大學理科大學物理科[物理學]

[1] When is heat engine called reversible? Show that all reversible engines are equally efficient.

[2] Calculate the action between two small magnets of moments M and M' placed in one line, the centers being at a distance r from each other.

[3] What are the characteristics of \alpha, \beta and \gamma rays from radioactive substances?

[4] Calculate the velocity of sound in hydrogen at t=20.7^{\circ}\mbox{C} by the formula v=\dfrac{v_0}{\sqrt{p}}\sqrt{1+\alpha 
 t} where v_0=332\mbox{m}/\mbox{sec} the velocity of sound in air at 0^{\circ}\mbox{C}, \alpha=0.0037, the coeff of thermal expansion, \sqrt{p}=0,264, p being the density of hydrogen relative to air.