Homework Statement
This isn't really homework, but a question I came upon when doing my homework.
How can I go from an integral with limits 0 and a:
\int_0^a f(x) dx
to something with limits 0 and \infty (still giving the same answer)
c\int_0^\infty f(u) du
, where c is...
I tried another approach after some hint from another student, setting \epsilon_1' = 0 and \epsilon_2' = \epsilon_2 - \epsilon_1. Then the temperature dependence doesn't disappear when I derivate to find U and Cv, but the expressions doesn't look very nice. This is part 1 of a problem, so I...
I really don't know if you can solve this without using any formulas, since there seems to be a lot of factors. These are the formulas I would use
W = \sqrt{\frac{2\epsilon_r\epsilon_0 V_j}{q}\left(\frac{1}{N_a} + \frac{1}{N_d} \right)}, where
V_j = V_0 = \frac{kT}{q}\ln \left(...
The speed of the water surface in the tank is related to how much water that leaves the tank per second. What's the relation between the amount leaving the tank and the change in the height of water in the tank? The direction ("speed + direction" = velocity) is -y, or downwards, since the...
The given problem:
The permitted energy values for a massless (or ultrarelativistic) particle (kinetic energy much larger than rest energy) in a 3-dimensional cubic box of volume V = L^3, can be expressed in terms of quantum numbers n_{x}, n_{y} and n_{z}:
\epsilon = \frac{hc\sqrt{n_x^2 +...