Chapter 13, Problem 63A

Interpretation Introduction

Interpretation: The reason for the expanded raft as the temperature increases is to be explained.

Concept introduction:

Kinetic energy is a type of energy that a moving object or particle possesses. Among, liquids, solids, and gases, gases possess the highest kinetic energy.

Answer to Problem 63A

The average kinetic energy of the gas molecules inside the raft increase because of an increase in temperature.

Explanation of Solution

The relationship between kinetic energy and temperature is as follows:

  $E_k=\frac{3}{2}{k}_{B}T$

Here, $E_k$ is kinetic energy, $k_B$ is Boltzmann’s constant, and $T$ is temperature.

Thus, from the above expression, kinetic energy is directly proportional to temperature.

The raft expands because of the air particles' increased kinetic energy and speed as the temperature rises. The air particles slow down when the temperature drops, resulting in a loss of kinetic energy, which prevents the raft from inflating completely.