Chapter 10, Problem 10.74PAE

Interpretation Introduction

Interpretation:

Entropy changes in a process where first a sample of water is heated until it boils and then water vapor is heated from 400 K to 500 K at constant volume should be explained.

Concept Introduction:

Entropy is defined as the measure of randomness or disorder in a system.

Entropy of a system is defined statistically on a microscopic level. In statistical mechanics the number of microstates or energy states that is the number of ways in which these microscopic particles acquire same energy is determined.

The number of microstates for a particular energy is denoted as Omega (O). And the entropy is then related to number of microstates by the equation:

$S=k_{\text{B}}\ln \Omega$

Where, $k_{\text{B}}$ is Boltzmann’s constant.

More random arrangements of particles of a system would increase the number microstates possible for the system. And so entropy of any system increases if it moves towards more random distribution of particles constituting the system.

Entropy of a system varies with temperature. In a system like water molecules are constantly in motion due to the energy available to them.

When a system is heated to a higher temperature, the total energy available to the molecules increases and some portion of molecules can now move at higher speeds. The system can now distribute its energy in more number of ways. Hence heating a system increases it entropy.

Solution:

a)

Yes when a sample of water is heated its entropy increases.

b)

Only the speed of individual molecules increases on raising the temperature. Since the overall volume is constant the positions that the molecules occupy remains same.

c)

On heating the system to a higher temperature, the total energy available to the molecules has increased, which increases the entropy.

d)

Yes when a sample of water vapor is heated from 400 K to 500 K at constant volume.

b)

Only the speed of individual molecules increases on raising the temperature. Since the overall volume is constant the positions that the molecules occupy remains same.

c)

On heating the system to a higher temperature, the total energy available to the molecules has increased, which increases the entropy.

a)