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MMLU-Pro / 3656 / The barometric formula relates the pressure of a gas of molar mass M at an…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

The barometric formula relates the pressure of a gas of molar mass MM at an altitude hh to its pressure p0p_0 at sea level. Derive this relation by showing that the change in pressure dp\mathrm{d} p for an infinitesimal change in altitude dh\mathrm{d} h where the density is ρ\rho is $\mathrm{d} p=-\rho g \mathrm{~d} h$. Remember that ρ\rho depends on the pressure. Evaluate the external atmospheric pressure at a typical cruising altitude of an aircraft (11 km) when the pressure at ground level is 1.0 atm.
Plain-text mathematical notation (without MathML)
The barometric formula relates the pressure of a gas of molar mass M at an altitude h to its pressure p₀ at sea level. Derive this relation by showing that the change in pressure dp for an infinitesimal change in altitude dh where the density is ρ is $\mathrm{d} p=-\rho g \mathrm{~d} h$. Remember that ρ depends on the pressure. Evaluate the external atmospheric pressure at a typical cruising altitude of an aircraft (11 km) when the pressure at ground level is 1.0 atm.
Original LaTeX notation
The barometric formula relates the pressure of a gas of molar mass $M$ at an altitude $h$ to its pressure $p_0$ at sea level. Derive this relation by showing that the change in pressure $\mathrm{d} p$ for an infinitesimal change in altitude $\mathrm{d} h$ where the density is $\rho$ is $\mathrm{d} p=-\rho g \mathrm{~d} h$. Remember that $\rho$ depends on the pressure. Evaluate the external atmospheric pressure at a typical cruising altitude of an aircraft (11 km) when the pressure at ground level is 1.0 atm.

category

chemistry

options

  1. 0.33
  2. 0.72
  3. 0.25
  4. 0.58
  5. 1.00
  6. 1.15
  7. 0.50
  8. 0.85
  9. 0.95
  10. 0.40

src

scibench-atkins

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Source and history

upstream_id / Original problem ID
3656
task_id
5bdedcbc-7e16-584c-bb69-cf8dde6ba38f
task_key
default--test--3656
task_revision_id
1
config / split
default / test

Official source

initial import