VoC (b) When will its temperature be 12°C? 46 min Need Help?Read It s. O -12 poi

Question

VoC (b) When will its temperature be 12°C? 46 min Need Help?Read It s. O -12 points CET8 3.8.019 Notes O Ask Your The rate of change of atmospheric pressure P with respect to altitude h is proportional to P, provided that the temperature is At a specific temperature the pressure is 103.7 kPa at sea level and 89.2 kPa at h-1,000 m. (Round your answers to one decimal place.) (a) What is the pressure at an altitude of 2500 m? kPa (b) What is the pressure at the top of a mountain that is 6563 m high? kPa ad Notes Ask Yout Teac O 3/8 points | Previous Answers SCalcET8 3.8.021 (a) If $2000 is invested at 2% interest, find the value of the investment at the end of 7 years if the interest is compounded as follows. (Round your answers to the nearest cent.) (i) annually 2297.37 (ii) semiannually

Explanation / Answer

Question 8.

Let say pressure P and height is h

dP/dh = kP

dP/P = kdh

ln [P/P0] = kh

P = P0 ekh

so for h = 0 , P0 = 103.7 kPa

so for h = 1000 m , P1000 = 89.2 kPa

ln (89.2/103.7) = k * 1000

k = -1.5062 x 10-4  m-1

(a) At h = 2500 m

ln [P/P0] = kh

ln [P/P0] = (-1.5062 x 10-4) h

ln [P/103.7] = (-1.5062 x 10-4) * 2500 = -0.37655

P/103.7 = 0.68622

P (2500m) = 71.16 kPa

(b) Here h = 6563 m high

ln [P/P0] = kh

ln [P/P0] = (-1.5062 x 10-4) h

ln [P/103.7] = (-1.5062 x 10-4) * 6563 = -06895

P/103.7 = 0.37212

P = 38.59 kPa

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