Chapter 5, Problem 156CP

(a)

Interpretation Introduction

Interpretation:

Rising of argon balloon while heating should be explained and the temperature at which the balloon floated should be determined.

Concept introduction:

• According to Charles’s law at constant pressure and number of moles, volume of a gas container is directly proportional to the temperature of gas.

            Mathematically this law can be written as,

$\begin{array}{l}V\propto T\\ \text{V}\text{=}\text{b}\text{T}\end{array}$

            Where T is temperature and b is proportionality constant.

• Equation for density is,

$\text{Density}\text{=}\frac{\text{Mass}}{\text{Volume}}$

Density and volume are inversely proportional.  As temperature increases, on accordance with Charles’s law volume will increase and density must be decreases

• Ideal gas equation in terms of Density,

$\text{Density}\text{=}\frac{\text{Pressure}\text{×}\text{Molecular mass}}{\text{R}\text{×}\text{Temperature}}$

$\text{Density}\text{of}{\text{air,d}}_{\text{air}}\text{=}\frac{\text{P}\text{×}\text{MM}{}_{\text{air}}}{\text{R}\text{×T}}\text{,where}\text{MM}{}_{\text{air}}\text{=average}\text{molar}\text{mass}\text{of}\text{air}$

To explain: Rising of argon balloon when it is heated.

(b)

Interpretation Introduction

Interpretation:

Rising of argon balloon while heating should be explained and the temperature at which the balloon floated should be determined.

Concept introduction:

• According to Charles’s law at constant pressure and number of moles, volume of a gas container is directly proportional to the temperature of gas.

            Mathematically this law can be written as,

$\begin{array}{l}V\propto T\\ \text{V}\text{=}\text{b}\text{T}\end{array}$

            Where T is temperature and b is proportionality constant.

• Equation for density is,

$\text{Density}\text{=}\frac{\text{Mass}}{\text{Volume}}$

Density and volume are inversely proportional.  As temperature increases, on accordance with Charles’s law volume will increase and density must be decreases

• Ideal gas equation in terms of Density,

$\text{Density}\text{=}\frac{\text{Pressure}\text{×}\text{Molecular mass}}{\text{R}\text{×}\text{Temperature}}$

$\text{Density}\text{of}{\text{air,d}}_{\text{air}}\text{=}\frac{\text{P}\text{×}\text{MM}{}_{\text{air}}}{\text{R}\text{×T}}\text{,where}\text{MM}{}_{\text{air}}\text{=average}\text{molar}\text{mass}\text{of}\text{air}$

To explain: Rising of argon balloon when it is heated.