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MMLU-Pro / 4365 / 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 pressure difference between the top and bottom of a laboratory vessel of height 15 cm.
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 pressure difference between the top and bottom of a laboratory vessel of height 15 cm.
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 pressure difference between the top and bottom of a laboratory vessel of height 15 cm.

category

chemistry

options

  1. $1.8 \times 10^{-5}$
  2. $1.7 \times 10^{-5}$
  3. $2.0 \times 10^{-5}$
  4. $1.0 \times 10^{-5}$
  5. $1.5 \times 10^{-5}$
  6. $1.2 \times 10^{-5}$
  7. $2.5 \times 10^{-5}$
  8. $1.9 \times 10^{-5}$
  9. $1.3 \times 10^{-5}$
  10. $2.2 \times 10^{-5}$

src

scibench-atkins

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Source and history

upstream_id / Original problem ID
4365
task_id
1a844f59-7a01-5c02-9420-96647f123315
task_key
default--test--4365
task_revision_id
1
config / split
default / test

Official source

initial import