Derive an expression for the gravitational potential energy U(r) of the object-earth system as a function of the object's distance from the center of the earth. Take the potential energy to be zero when the object is at the center of the earth.

8.29 two streams containing pyridine and acetic acid at 25°c are mixed and fed into a heat exchanger. due to the heat-of-mixing effect, it is desired to reduce the temperature after mixing to 25°c using a stream of chilled ethylene glycol as indicated in the diagram. calculate the mass flow rate of ethylene glycol needed. the heat capacity of ethylene glycol at these conditions is approximately 2.8 kj/(kg k), and the enthalpy change of mixing (δmixh) is given below.

The results of huy's eye exam show that he is nearsighted. which explanation should huy expect to hear? "you need convex lenses to shorten the distance that light takes to focus in your eyes." "you need concave lenses to shorten the distance that light takes to focus in your eyes." "you need convex lenses to lengthen the distance that light takes to focus in your eyes." "you need concave lenses to lengthen the distance that light takes to focus in your eyes."

Hurry! how much heat is absorbed by a 72g iron skillet when its temperature rises from 11°c to 23°c?