Chapter 9, Problem 9.28CP

(a)

Interpretation Introduction

Interpretation:

The apparatus has to be redrawn if the temperature is increased from $\text{300}\text{K}\text{to}\text{450}\text{K}$ at constant pressure.

Concept introduction:

Charles’s law: States that volume is directly proportional to temperature when the gas is held at constant pressure and number of molecules.

$\begin{array}{l}\text{V}\propto \text{T}\\ \text{V}\text{=}\text{Constant}\text{×}\text{T}\\ \frac{{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The apparatus has to be redrawn if the pressure is increased from $\text{1}\text{atm}\text{to}\text{2}\text{atm}$ at constant temperature.

Concept introduction:

Boyle’s law:

At fixed temperature, the volume of a fixed amount of gas is inversely proportional to the pressure exerted by the gas.

$\begin{array}{l}\text{P}\propto \frac{\text{1}}{\text{V}}\left(\text{n}\text{,}\text{T}\text{will}\text{be}\text{constant}\right)\\ \text{PV}\text{=}\text{constant}\\ {\text{P}}_{\text{1}}{\text{V}}_{\text{1}}\text{=}{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The apparatus has to be redrawn if the temperature is decreased from $\text{300}\text{K}\text{to}200\text{K}$ and the pressure is decreased from $3\text{atm}\text{to}\text{2}\text{atm}$.

Concept introduction:

General Gas Law:

Combining Charles’s law and Boyle’s law we get the General gas law or combined gas law.

$\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$