In 25 samples of size n = 7, the average value of the sample means is x=2.812 cm for the dimension of interest, and the mean of the ranges of the samples is r=0.023 cm. determine the lower and upper control limits for the (a) r chait and (b) r chart.

Air (c-1.006 kj/kg.k, r-0.287 kj/kg.k) enters a nozzle steadily at 280 kpa and 77°c with a velocity of 50 m/s and exits at 85 kpa and 320 m/s. the heat losses from the nozzle to the surrounding medium at 20°c are estimated to be 3.2 kj/kg. determine (a) the exit temperature and (b) the total entropy change for this process. solve this problem using constant specific heats.