Chapter 12, Problem 12.1P

Interpretation Introduction

(a)

Interpretation:

The number of variables, in addition to the mass of each component and the temperature that must be specified to fully determine the intensive state of the system should be determined.

Concept Introduction:

The physical properties of the materials or a system can frequently be classified as either intensive or extensive, as how the property alters when the size or the extent of the system transforms. An intensive property is the one whose magnitude does not dependent on the size of the system while the extensive property is the one whose extent is additive for subsystems.

Intensive property is a physical attribute of the system which does not depend on the size or the quantity of material present in the system. For instance, temperature, refractive index, density, hardness of object etc.

On the contrary, the extensive attribute is additive for the subsystems, which means the system could be separated into any quantity of the subsystems, and the extensive attribute calculated for every subsystem; the value of the attribute for the system would be the total sum of the attribute for each of the subsystem. For instance, mass, volume, etc.

The minimum number of intensive variables which need to be defined in order to define the system is 2.

Given:

A closed vessel of fixed volume having equal masses of water, ethanol, and toluene at 70 °C. Three phases (two liquid and one vapor) are present.

Calculation:

The number of intensive variables which need to be specified can be calculated by using the following formula:

  $F=C-P+2$

where, C is number of components in the system (= 3), P is number of phases in the system (= 3), F is the degree of system

  $F=3-3+2=2$

The degree of freedom is 2. Hence, the minimum number of intensive variables which need to be defined to define the system is 2.

Answer to Problem 12.1P

The minimum number of intensive variables which need to be defined in order to define the system is 2.

Explanation of Solution

Given:

A closed vessel of fixed volume having equal masses of water, ethanol, and toluene at 70 °C. Three phases (two liquid and one vapor) are present.

Calculation:

The number of intensive variables which need to be specified can be calculated by using the following formula:

  $F=C-P+2$

where, C is number of components in the system (= 3), P is number of phases in the system (= 3), F is the degree of system

  $F=3-3+2=2$

The degree of freedom is 2. Hence, the minimum number of intensive variables which need to be defined to define the system is 2.

Interpretation Introduction

(b)

Interpretation:

Number of variables, in addition to the mass of each component and the temperature that must be specified to fully determine the extensive state of the system.

Concept Introduction:

The physical properties of the materials or a system can frequently be classified as either intensive or extensive, as how the property alters when the size or the extent of the system transforms. An intensive property is the one whose magnitude does not dependent on the size of the system while the extensive property is the one whose extent is additive for subsystems.

Intensive property is a physical attribute of the system which does not depend on the size or the quantity of material present in the system. For instance, temperature, refractive index, density, hardness of object etc.

On the contrary, the extensive attribute is additive for the subsystems, which means the system could be separated into any quantity of the subsystems, and the extensive attribute calculated for every subsystem; the value of the attribute for the system would be the total sum of the attribute for each of the subsystem. For instance, mass, volume, etc.

Answer to Problem 12.1P

There is no requirement to define the additional variables to describe the extensive state of the system.

Explanation of Solution

Given:

A closed vessel of fixed volume having equal masses of water, ethanol, and toluene at 70 °C. Three phases (two liquid and one vapor) are present.

The external variables do not help in determining the state of the system. These variables only aid us to characterize the system.

Interpretation Introduction

(c)

Interpretation:

Whether the increase in temperature of the system to 72 °C will affect any, intensive or extensive coordinates of the system or not.

Concept Introduction:

The physical properties of the materials or a system can frequently be classified as either intensive or extensive, as how the property alters when the size or the extent of the system transforms. An intensive property is the one whose magnitude does not dependent on the size of the system while the extensive property is the one whose extent is additive for subsystems.

Intensive property is a physical attribute of the system which doesn’t depend on the size or the quantity of material present in the system. For instance, temperature, refractive index, density, hardness of object etc.

On the contrary, the extensive attribute is additive for the subsystems, which means the system could be separated into any quantity of the subsystems, and the extensive attribute calculated for every subsystem; the value of the attribute for the system would be the total sum of the attribute for each of the subsystem. For instance, mass, volume, etc.

The extensive property does not affect the system if the temperature of the system is raised from 70 °C to 72 °C, as these properties only distinguish the system yet to describe the system, we need intensive variables.

Given:

A closed vessel of fixed volume having equal masses of water, ethanol, and toluene at 70 °C. Three phases (two liquid and one vapor) are present.

Explanation:

The temperature of the system is raised to 72 °C. Suppose any intensive or extensive variables of the system stay unchanged.

The system can be described at any temperature (T) with the utilization of intensive attributes, but as the temperature is raised, it will cause an alteration in the intensive property which isindependent of mass. If the intensive property of the system remains unchanged, it can lead to unfeasibility of the process that the system undergoes.

Answer to Problem 12.1P

The extensive property does not affect the system if the temperature of the system is raised from 70 °C to 72 °C, as these properties only distinguish the system yet to describe the system, we need intensive variables.

Explanation of Solution

Given:

A closed vessel of fixed volume having equal masses of water, ethanol, and toluene at 70 °C. Three phases (two liquid and one vapor) are present.

The temperature of the system is raised to 72 °C. Suppose any intensive or extensive variables of the system stay unchanged.

The system can be described at any temperature (T) with the utilization of intensive attributes, but as the temperature is raised, it will cause an alteration in the intensive property which isindependent of mass. If the intensive property of the system remains unchanged, it can lead to unfeasibility of the process that the system undergoes.