Cuesta College, San Luis Obispo, CA
The highest and lowest points[*] in the 48 contiguous states of the U.S are Mt. Whitney (4,421 m above sea level) and Badwater Basin (85 m below sea level). Assume that the variation of gravitational constant g and the density of air (ρair = 1.3 kg/m3) with elevation is negligible. The air pressure on top of Mt. Whitney is __________ less than the air pressure in Badwater Basin.
(A) 6.6×102 Pa.
(B) 4.5×104 Pa.
(C) 5.3×104 Pa.
(D) 1.024×105 Pa.
Correct answer (highlight to unhide): (C)
For static fluids, the energy density relation between pressure difference ∆P and elevation change ∆y is given by:
0 = ∆P + ρ·g·∆y.
The difference in pressure ∆P between Mt. Whitney and Badwater Basin is then:
∆P = –ρ·g·∆y,
∆P = –ρ·g·(yWhitney – yBadwater),
∆P = –(1.3 kg/m3)·(9.80 m/s2)·((+4,421 m) – (–85 m)),
∆P = –(1.3 kg/m3)·(9.80 m/s2)·(+4,506 m),
∆P = –57,406.44 Pa,
such that the difference in pressure between Mt. Whitney and Badwater Basin (to two significant figures) is 5.7×104 Pa (the negative sign in the above calculation denotes that the air pressure at Mt. Whitney is less than the air pressure in Badwater Basin).
(Response (A) is ρ·g·(yWhitney/yBadwater); response (B) is the absolute air pressure atop Mt. Whitney; and response (D) is the absolute air pressure in Badwater Basin.)
Sections 70854, 70855, 73320
Exam code: quiz05bL8D
(A) : 17 students
(B) : 0 students
(C) : 43 students
(D) : 5 students
Success level: 66%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.63