Throughout this question, assume that the universe the universe only contains matter and a possible cosmological constant. use the definition of the density parameter to show that at any epoch we can write the matter density as constant-ω0h0 given that in any realistic cosmology s2mat ~ 1 at early times, compute the hubble parameter at decoupling (zdec 1000) as a fraction of its present value. as the only important characteristic scale in the young universe, the hubble length ch gives the characteristic scale of the first peak in the microwave background. in a spatially-flat cosmology with a cosmological constant, the present physical distance to an object with z »> 1 is given approximately by 0 [if you wish, you can verify this approximation by numerical integration along the lines of problem a2.4.] by considering the angular diameter distance, demonstrate that the angle subtended by the hubble length at decoupling is approximately inde- pendent of s2o in spatially-flat cosmologies, and compute its value in degrees. this demonstrates that the peak position is nearly independent of 2a for spatially-flat geometries, the approximations being the formula for aoto above and the assump- tion that the universe is perfectly matter dominated at last-scattering.

An internally reversible refrigerator has a modified coefficient of performance accounting for realistic heat transfer processes of where qin is the refrigerator cooling rate, qout is the heat rejection rate, and is the power input. show that copm can be expressed in terms of the reservoir temperatures tc and th, the cold and hot thermal resistances rt,c and rt,h, and qin, as where rtot rt,c rt,h. also, show that the power input may be expressed as 1.39 a household refrigerator operates with cold- and hot-temperature reservoirs of tc 5 c and th 25 c, respectively. when new, the cold and hot side resistances are rc,n 0.05 k/w and rh,n 0.04 k/w, respectively. over time, dust accumulates on the refrigerator’s condenser coil, which is located behind the refrigerator, increasing the hot side resistance to rh,d 0.1 k/w. it is desired to have a refrigerator cooling rate of qin 750 w. using the results of problem 1.38, determine the modified coefficient of performance and the required power input w under (a) clean and (b) dusty coil conditions. internally reversible refrigerator qout qin w high-temperature reservoir low-temperature reservoir th th,i tc,i tc high-temperature side resistance low-temperature side resistance w qin th tc qinrtot tc qinrtot copm tc qinrtot th tc

What is an aquifer for science class

What is a view of science and psychology that says the value of knowledge depends on its usefulness? a. pragmatism b. psychotherapy c. physiology