PROBLEMS AND SOLUTIONS

IN

THERMAL PHYSICS [For B.Sc. (Pass Course) and B.S. (Honours)]

Dr. Muhammad Ashfaq Ahmed Professor and Dean,

Faculty of Basic Sciences,

University of Balochistan,

Quetta.

According to Latest Syllabus Prescribed by all the

Universities of Pakistan

ALLIED BOOK CENTRE

KABEER STREET # 2, URDU BAZAR, LAHORE

Phone (042) 37241238, 37325451

ii

iii

Preface

The numerical problem solving has become an integral

part of all undergraduate Physics Courses. This book has been

designed to meet the requirement of B.Sc. (Pass) and B.S.

(Honours) students of Pakistani Universities according to the

latest prescribed syllabus. A careful study of these solved

numerical problems will help in better understanding of the

relevant physical principles. The problems have been selected

from recent examination papers of various universities and

cover a wide spectrum of topics in Thermal Physics. One can

not claim much originality in such type of book. A large

number of books have been consulted during the preparation of

this work. I am very grateful to authors and publishers of these

books. This book can serve as a companion to any standard text

book on Thermal Physics. I have made my best efforts to make this work free from

errors but there will be still some errors which might have

escaped from my attention. The readers are requested to point

out any conceptual and typographical errors so that the same

can be eliminated in next edition. The suggestions for further

improvement of the book will be greatly appreciated and

incorporated in the next edition with due acknowledgement.

November, 2010. Muhammad Ashfaq Ahmed

iv

List of Abbreviations

A Annual Examination

S Supplementary Examination

B.U. University of Balochistan, Quetta.

K.U. University of Karachi, Karachi.

P.U. University of the Punjab. Lahore.

B.Sc. Bachelor of Science

F.P.S.C. Federal Public Service Commission

B.P.S.C. Balochistan Public Service Commission

v

TABLE OF CONTENTS

1. Temperature and Heat Page No. 1-1 Temperature Scales 01

1-2 Linear Expansion 05

1-3 Superficial or Surface Expansion 08

1-4 Cubical or Volumetric Expansion 09

1-5 Specific heat 13

1-6 Thermal Conduction 17

2. Thermal Properties of Matter 2-1 Boyle’s Law 19

2-2 Charles’s Law 21

2-3 Gay-Lussac’s Law 22

2-4 The Ideal Gas Law 24

2-5 The Internal Energy of an Ideal

Gas 37

2-6 The Kinetic Theory of Gases 43

2-7 The Mean Free Path 53

Additional Problems 58

3. The First Law of Thermodynamics 3-1 The First Law of Thermodynamics 59

3-2 Heat Capacities of an Ideal Gas 62

3-3 Work Done on or by an Ideal Gas

(a) Work Done at Constant Volume 66

(b) Work Done at Constant Pressure 67

(c) Work done at Constant Temperature 69

(d) Work Done at Thermal Isolation

or Adiabatic Conditions 71

Additional Problems 81

vi

4. The Second Law of Thermodynamics

4-1 Efficiency of a Heat Engine 82

4-2 Coefficient of Performance of a

Refrigerator Engine 95

Additional Problems 98

5. Entropy 5-1 Introduction 100

5-2 Entropy Change for an Ideal Gas

(a) Isothermal Process 108

(b) Isobaric Process 110

(c) Isochoric Process 112

5-3 Miscellaneous 113

Additional Problems 117