Chapter 15, Problem 29CR

Interpretation Introduction

(a)

Interpretation:

The new volume of the given sample on increasing the temperature from $35{}^{°}\text{C}$ to $55{}^{°}\text{C}$ is to be calculated.

Concept Introduction:

The Charles’ law states that the volume of a given ideal gas system is directly proportional to the absolute temperature of the system at constant pressure. The Charles’ law is represented as:

$\text{V}\propto \text{T}$

Where,

• $\text{V}$ represents the volume of the system.
• $\text{T}$ represents the temperature of the system.

The relation between the initial and final volume of an ideal gas system on changing the temperature of the system at constant pressure is given as:

$\frac{{\text{V}}_1}{{\text{T}}_1}=\frac{{\text{V}}_2}{{\text{T}}_2}$

Where,

• ${\text{V}}_1$ represents the initial volume of the system.
• ${\text{T}}_1$ represents the initial temperature of the system.
• ${\text{V}}_2$ represents the final volume of the system.
• ${\text{T}}_2$ represents the final temperature of the system.

Interpretation Introduction

(b)

Interpretation:

The new volume of the given sample on decreasing the temperature from $25{}^{°}\text{C}$ to $-196{}^{°}\text{C}$ is to be calculated.

Concept Introduction:

The Charles’ law states that the volume of a given ideal gas system is directly proportional to the absolute temperature of the system at constant pressure. The Charles law is represented as,

$\text{V}\propto \text{T}$

Where,

• $\text{V}$ represents the volume of the system.
• $\text{T}$ represents the temperature of the system.

The relation between the initial and final volume of an ideal gas system on changing the temperature of the system at constant pressure is given as:

$\frac{{\text{V}}_1}{{\text{T}}_1}=\frac{{\text{V}}_2}{{\text{T}}_2}$

Where,

• ${\text{V}}_1$ represents the initial volume of the system.
• ${\text{T}}_1$ represents the initial temperature of the system.
• ${\text{V}}_2$ represents the final volume of the system.
• ${\text{T}}_2$ represents the final temperature of the system.