Combined-science Textbooks (13)

A completely saturated clay sample is loaded in a cell test by a vertical stress of \(80 \mathrm{kPa}\). Due to this load the cell pressure increases by \(20 \mathrm{kPa}\). If the soil were perfectly elastic, what would then be the increment of the pore pressure?

Imagine the Earth is on the surface of a sphere whose radius is equal to the sun-Earth distance, \(1.50 \times 1011 \mathrm{~m}\). If the total radiant flux from the sun (W) calculated above is evenly distributed over the surface of that imaginary sphere, what is the average flux in \(\mathrm{W} \mathrm{m}^{-2}\) ?

The critical point of a Flory-Huggins solution. For the mixing of a polymer \(A\left(N_{A}=10^{4}\right)\) with a small molecule \(B\) ( \(N_{B}=1\) ), compute the critical volume fraction \(\phi_{c}\) and the critical exchange parameter \(\chi_{c}\).

Show that the criterion for a density matrix to be a pure state is $$ \rho^{2}=\rho . $$

Find the lowest three values of \(k^{2}\) for which the two-dimensional Helmholtz equation $$ \nabla^{2} \phi+k^{2} \phi=0 $$ has a nontrivial solution inside a \(30^{\circ}-60^{\circ}-90^{\circ}\) right triangle whose sides are \(a, a \sqrt{3}\), and \(2 a .\) The boundary condition is that \(\phi=0\) on the perimeter of the triangle.