Chapter 5, Problem 93QAP

Interpretation Introduction

Interpretation:

The diameter of the spherical hydrogen filled balloon needs to be calculated, if the balloon and balloonist together weigh 168 kg and if the temperature is 22 ⁰C and pressure is 758 mm Hg.

Concept introduction:

According to the ideal gas law volume i.e. V, pressure i.e. P, number of moles i.e. m, temperature i.e. t and universal gas constant i.e. R is interrelated as below:

$\text{PV = nRT}$

When gases are placed at two different conditions, then to determine the changed variable, combined gas law is used. Below is the formula of combined gas law:

$\stackrel{\text{Gas 1}}{\overbrace{\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{n}}_{\text{1}}{\text{T}}_{\text{1}}}}}\text{=}\stackrel{\text{Gas2}}{\overbrace{\frac{{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{n}}_{\text{2}}{\text{T}}_{\text{2}}}}}$

Here,

• P₁ and P₂ are the pressure of gases
• V₁ and V₂ and volume of gases
• n₁ and n₂ number of moles
• T₁ and T₂ are the temperature of gases

Formula to calculate the density is:

$d=MM\left(\frac{P}{RT}\right)$

Here d is the density, MM is the molar mass of gas, P is pressure, R is gas constant and T is temperature.

And the formula to calculate the volume of sphere = $\frac{4}{3}\pi r^3$. Here r is the radius of sphere.