Suppose you wanted to "pull an Einstein," and create a static universe  in which the gravitational attraction of matter is exactly balanced by the gravitational repulsion of dark energy with equation-of-state parameter − 1/ 3 < wq < − 1 and energy density εq.

What is the necessary matter density (εm) required to produce a static universe, expressed in terms of εq and wq?

Will the curvature of this static universe be negative or positive?

What will be its radius of curvature, expressed in terms of εq and wq?

Ineed extreme for task 2. my student number is 571721. many to whoever solves this correctly, im in debt to you.

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

The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. what is the specific heat ratio? show the math steps .