Physics quiz question: Caliente Mountain air pressure

Physics 205A Quiz 5, fall semester 2012
Cuesta College, San Luis Obispo, CA

"CalienteMountain"
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 ρ_air = 1.3 kg/m³ with elevation is negligible. (P_atm = 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 = (P_Caliente – P_{sea level}) + ρ_air·g·(y_Caliente – y_{sea level}),

where the air pressure at sea level is 101.3 kPa = 1.013×10⁵ Pa, such that:

P_Caliente = P_{sea level} – ρ_air·g·(y_Caliente – y_{sea level}),

P_Caliente = 1.013×10⁵ Pa – (1.3 kg/m³)·(9.80 m/s²)·((+1,556 m) – (0 m)),

P_Caliente = 1.013×10⁵ Pa – 0.20×10⁵ Pa = 0.81×10⁵ Pa = 8.1×10⁴ Pa.

(Response (A) is ρ_air·g·∆y, which is the relative pressure decrease between sea level and Caliente Mountain; response (C) is P_{sea level} + ρ_air·g·(y_Caliente – y_{sea level}); response (D) is (1/2)·ρ_air·(∆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