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Chapter 1: Problem 55

Find a mathematical model for the verbal statement. For a constant temperature, the pressure \(P\) of a gas is inversely proportional to the volume \(V\) of the gas.

Short Answer

Expert verified
The mathematical model for the verbal statement 'the pressure \(P\) of a gas is inversely proportional to the volume \(V\) of the gas' is \(PV = k\) where \(k\) is a constant.

Step by step solution

01

- Understanding the verbal statement

The statement says 'the pressure \(P\) of a gas is inversely proportional to the volume \(V\) of the gas'. This means that as the volume increases, the pressure decreases and vice versa.
02

- Writing the proportionality relationship

An inversely proportionate relationship can be written as \(P \propto \frac{1}{V}\). This means \(P\) is directly proportional to \(\frac{1}{V}\).
03

- Converting the proportionality formula to an equation

To convert the proportionality formula into an equation, introduce a constant of proportionality \(k\), thus the formula becomes \(P = k \times \frac{1}{V}\) or simply \(PV = k\)

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