Question

Boyle's Law Boyle's Law says that the volume $V$ of a gas at constant temperature increases whenever the pressure $P$ decreases, so that $V$ and $P$ are inversely proportional. If $P=14.7 \mathrm{lb} / \mathrm{in}^{2}$ when $V=1000 \mathrm{in}^{3},$ then what is $V$ when $P=23.4 \mathrm{lb} / \mathrm{in}^{2} ?$

Name: Problem 66, Chapter 1: Thomas Calculus
Uploaded: 2019-05-01T00:04:30-08:00
Duration: 1 min 57 s
Channel: Karl Schaefer
Description: Boyle's Law Boyle's Law says that the volume V of a gas at constant temperature increases whenever the pressure P decreases, so that V and P are inversely proportional. If P=14.7 lb / in^2 when V=1000 in^3, then what is V when P=23.4 lb / in^2 ?

   Boyle's Law Boyle's Law says that the volume $V$ of a gas at constant temperature increases whenever the pressure $P$ decreases, so that $V$ and $P$ are inversely proportional. If $P=14.7 \mathrm{lb} / \mathrm{in}^{2}$ when $V=1000 \mathrm{in}^{3},$ then what is $V$ when $P=23.4 \mathrm{lb} / \mathrm{in}^{2} ?$

Thomas Calculus

George B. Thomas Jr. 14th Edition

Chapter 1, Problem 66

Instant Answer

Solved by Expert Karl Schaefer

05/01/2019

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This can be represented mathematically as $V = \frac{k}{P}$, where $k$ is a constant. Show more…

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Boyle's Law Boyle's Law says that the volume $V$ of a gas at constant temperature increases whenever the pressure $P$ decreases, so that $V$ and $P$ are inversely proportional. If $P=14.7 \mathrm{lb} / \mathrm{in}^{2}$ when $V=1000 \mathrm{in}^{3},$ then what is $V$ when $P=23.4 \mathrm{lb} / \mathrm{in}^{2} ?$

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Key Concepts

Boyle's Law

Boyle's Law is a principle in thermodynamics which states that for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. This means that if the pressure increases, the volume decreases in such a way that the product of pressure and volume remains a constant.

Inverse Proportionality

Inverse proportionality is a mathematical relationship where one variable increases as the other decreases. In the context of gas laws, this relationship indicates that the product of pressure and volume is constant when temperature is held fixed, so changes in pressure lead to corresponding inverse changes in volume.

Constant Temperature

Constant temperature is a condition where the thermal energy of the gas remains unchanged. This is a crucial requirement for applying Boyle's Law, as fluctuations in temperature can affect the behavior of the gas and alter the relationship between pressure and volume.

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