Cuesta College, San Luis Obispo, CA
Atandrus
wki.pe/File:CalienteMountain.JPG
The summit of Caliente Mountain (1,556 m above sea level), near New Cuyama, is the highest point in San Luis Obispo county[*]. Assume that the variation of gravitational constant g and the density of air ρair = 1.3 kg/m3 with elevation is negligible. (Patm = 101.3 kPa.) The air pressure at the summit is:
(A) 2.0×104 Pa.
(B) 8.1×104 Pa.
(C) 1.2×105 Pa.
(D) 1.6×106 Pa.
[*] wki.pe/Caliente_Mountain.
Correct answer (highlight to unhide): (B)
For static fluids, the energy density relation between pressure and changes in elevation is given by:
0 = ∆P + ρ·g·∆y,
0 = (PCaliente – Psea level) + ρair·g·(yCaliente – ysea level),
where the air pressure at sea level is 101.3 kPa = 1.013×105 Pa, such that:
PCaliente = Psea level – ρair·g·(yCaliente – ysea level),
PCaliente = 1.013×105 Pa – (1.3 kg/m3)·(9.80 m/s2)·((+1,556 m) – (0 m)),
PCaliente = 1.013×105 Pa – 0.20×105 Pa = 0.81×105 Pa = 8.1×104 Pa.
(Response (A) is ρair·g·∆y, which is the relative pressure decrease between sea level and Caliente Mountain; response (C) is Psea level + ρair·g·(yCaliente – ysea level); response (D) is (1/2)·ρair·(∆y)2.)
Sections 70854, 70855
Exam code: quiz05L4mN
(A) : 24 students
(B) : 15 students
(C) : 3 students
(D) : 10 students
Success level: 29%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.39
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