Chapter 13, Problem 11A

Interpretation Introduction

Interpretation:

The new pressure of helium gas have to be calculated.

Concept Introduction:

Boyle’s law: The pressure of a gas is inversely proportional to the volume of the gas at constant temperature.

The relationship between pressure and volume of a gas is expressed as-

  $\begin{array}{l}\mathrm{P}\propto \frac{1}{V}\\ \mathrm{or},PV=Constant\end{array}$ When T is constant.

The equation of Boyle’s law at constant temperature and amount of gas is

  $\begin{array}{l}{\mathrm{P}}_1{V}_1=P_2{V}_2\\ \frac{P_2}{{\mathrm{P}}_1}=\frac{V_1}{V_2}\end{array}$

Initial pressure = P₁ Final pressure = P₂

Initial volume = V₁ Final volume = V₂

Answer to Problem 11A

In first case, when volume is reduced to its half, final pressure will be doubled to the initial pressure. In the second case, when volume is not changing, pressure will not change.

Explanation of Solution

For case I:

Data given: V₁ = 2X

V₂ = X

  $\begin{array}{l}\frac{P_2}{P_1}=\frac{V_1}{V_2}\\ \frac{P_2}{P_1}=\frac{2X}{X}=2\\ P_2=2P_1\end{array}$

In first case, when volume is reduced to its half, final pressure will be doubled to the initial pressure.

For case II:

Data given: V₁ = V₂ = X

  $\begin{array}{l}\frac{P_2}{P_1}=\frac{V_1}{V_2}\\ \frac{P_2}{P_1}=\frac{X}{X}=1\\ P_2=P_1\end{array}$

In the second case, when volume is fixed, pressure will not change.