Chapter 5, Problem 5.59P

Interpretation Introduction

Interpretation:

The density of the air in the hot-air balloon at temperature $17°\text{C}$ and $\text{60 }°\text{C}$ is to be calculated.

Concept introduction:

According to Boyle’s law, the volume occupied by the gas is inversely proportional to the pressure at the constant temperature.

The relationship between pressure and volume can be expressed as follows,

$PV=\text{constant}$

Here, $P$ is the pressure and $V$ is the volume.

According to Charles's law, the volume occupied by the gas is directly proportional to the temperature at the constant pressure.

The relationship between pressure and temperature can be expressed as follows,

$V\alpha T$

Here, $T$ is the temperature and $V$ is the volume.

According to Avogadro’s law, the volume occupied by the gas is directly proportional to the mole of the gas at the constant pressure and temperature.

The relationship between volume and mole can be expressed as follows,

$\text{V }\alpha n$

Here, $n$ is the mole of the gas and $V$ is the volume.

The ideal gas equation can be expressed as follows,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas and $R$ is the gas constant.

The expression to calculate the density of the air is as follows,

$d=\frac{PM}{RT}$

Here, $P$ is the pressure, $M$ is the molecular mass, $T$ is the temperature, $d$ is the density of the air and $R$ is the gas constant.

The expression for the conversion of $\text{torr}$ and $\text{atm}$ is as follows:

$1\text{ atm}=\text{760 torr}$