Consider a cylinder initially filled with 9.23 10-4 m3 of ideal gas at atmospheric pressure. An external force is applied to slowly compress the gas at constant temperature to 1/4 of its initial volume. Calculate the work that is done. Note that atmospheric pressure is 1.013 105 Pa.

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

Aparticle of mass m is placed in a one-dimensional box of length l. the box is so small that the particle’s motion is relativistic, so that e p2/2m is not valid. (a) derive an expression for the energy levels of the particle using the relativistic energy–momentum relation and the quantization of momentum that derives from connement. (b) if the particle is an electron in a box of length l 1.00 1012 m, nd its lowest possible kinetic energy. by what percent is the nonrelativistic formula for the energy in error?

Ascientist is working with a new kind of quantum dot to make a dye. he is applying newton’s laws to the particle, but it seems to be breaking these laws of physics. which action will most likely the scientist study the particle’s motion? a. he needs to remember that the particle is too large for quantum analysis. b. he must continue to use newtonian mechanics, but he needs to learn more about the particle. c. he needs to use quantum mechanics, not newtonian mechanics, because this is a nanotechnology product. d. he must determine new physical laws that only apply to quantum dots.