Chapter 8, Problem 44E

Interpretation Introduction

Interpretation:

For a given balloon inflated to a volume of $\text{7}{\text{.00×10}}^{\text{2}}\text{ml}$  at a temperature of $\text{20}\text{.0°C}$ and its volume of gas should be determined when it is cooled at constant pressure to a temperature of $\text{1}{\text{.00×10}}^{\text{2}}\text{K}$.

Concept introduction:

A French physicist Jacques Charles introduced a gaseous law with interpreting the relationship between the temperature and volume of a gas at constant pressure. That is the behavior of gas towards the heat. This law is known as Charles’s law.

Charles’s law can be defined as,

A gas kept in the particular container at constant pressure. If the container of gas is heated, the gaseous particle is expanded and the volume of container is increased.  That is the volume of container is directly proportional to the temperature of gas. As increasing the temperature of a particular gas the volume of gas will expand. This direct relationship between the temperature and volume of gas is termed as Charles’s law.

Mathematically this law can be written as,

V $\propto$ T

V=bT

Where, T is temperature and b is proportionality constant.

By comparing two systems at different conditions,

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

This direct proportionality of temperature and volume can be can be explained as when temperature of a gas container is increases, the kinetic energy of atomic gaseous molecules is increases and the particles started to move from the initial position and the volume of gas container going to expand.