The following problem arises when experiments are done solids at high pressures. if the pressure is increased by an amount delta p, this being done under circumstances where the sample is thermally insulated and at a sufficiently slow rate that the process can be regarded as quasi-static, what is the resulting change of temperature delta t of the sample? if delta p is fairly small, derive an expression for delta t in terms of delta p, the absolute temperature t of the sample, its specific heat at constant pressure c_p (in ergs g^-1 deg^-1), its density rho (in g/cm^2), and its volume coefficient of thermal expansion alpha (in deg^-1).

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Awave travels at a speed of 5.2 m/s. if the distance between crests is 0.40 m, what is the frequency of the wave? use f=v/wavelength a. 13 hz b. 2.1 hz c. 0.077 hz d. 5.6 hz

Arotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. the outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. if the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?