Chapter 20, Problem 14A

A piston in an airtight pump is withdrawn so that the volume of the air chamber is increased five times. What is the change in pressure?

To determine

The change in pressure due to the given changes.

Answer to Problem 14A

The pressure is decreased by $\frac{1}{5}$ times of the initial pressure $P_1$ .

Explanation of Solution

Given:

Volume after withdrawn is increased 5 times.

Formula used:

Boyle’s law states that at constant temperature, the product of pressure and volume of the given mass of gas is constant.

The Boyle’s law is expressed as follows:

  $P_1{V}_1=P_2{V}_2$

Here, $P_1$ is the initial pressure, $V_1$ is the initial volume, $P_2$ is the final pressure, and $V_2$ is the final volume.

Calculation:

Let the volume of air chamber be $x$

So, the volume of air chamber after airtight pump is withdrawn = $5x$

Substitute $5x$ for $V_2$ andx for $V_1$

  $\begin{array}{c}{P}_2\left(5x\right)=P_{1}x\\ P_2=\frac{x}{5x}{P}_1\\ P_2=\frac{P_1}{5}\end{array}$

Conclusion:

Thus, the pressure is decreased by $\frac{1}{5}$ times of the initial pressure $P_1$ .