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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.

Four point charges each having charge q are located at the corners of a square having sides of length a. find symbolic expressions for the following. (a) the total electric potential at the center of the square due to the four charges (use any variable or symbol stated above along with the following as necessary: ke.) vtotal= (b) the work required to bring a fifth charge p from infinity to the center of the square (use any variable or symbol stated above along with the following as necessary: w=

An atom that has gained or lost electrons is called an _