An thin plate is positoned in the xy plane with corners at (0, 0), (10,0), (10, 30) and (0, 30). three edges are kept at a temperature of 0 kelvin whilst the y=0 edge is kept at 100 k. solve the laplace equation to find the temperature profile t(x, y) of the plate assuming steady state conditions. to do this, a) sketch out the problem. b) state or derive all general solutions of laplace's equation. releme c) define boundary conditions for all 4 edges including a formula for t (x,0) and hence explain which boundary conditions rule out which general solutions. d) express the remaining solution as a series and write down the fourier integral. e) solve the fourier integral in order to find the neccessary coefficients.

A30 kg weight lies on top of a massless piston of area a = 0.01 m2 the exterior air is at a (constant) p =1 atm and t = 27 c. the interior gas is 0.4 moles of (ideal) n2 and it has initial temperature 27.00 degrees c. 1. what is the initial pressure in the interior? a. 29.4 kpa b. 130.7 kpa c. 101.3 kpa the next three questions concern what happens when an amount of heat q is slowly added to the interior, raising the piston by 1 mm and raising the interior temperature to 27.40 c

A3.9 g aluminum foil ball with a charge of +4.1×10−9 c is suspended on a string in a uniform horizontal e⃗ field. the string deviates to the right and makes an angle of 30∘ with the vertical. part a part complete what information about the e⃗ field can you determine for this situation? what information about the field can you determine for this situation? only the magnitude of e⃗ only the direction of e⃗ both the magnitude and the direction of e⃗ none of the above previous answers correct part b determine the magnitude of the electric field. express your answer with the appropriate units. e e = nothing nothing request answer part c determine the direction of the electric field. determine the direction of the electric field. to the right to the left away from you toward you

Under normal conditions, describe how increasing the temperatures effects the solubility of a typical salt