Book edition 1st

Author(s) Daniel V. Schroeder

Pages 356 pages

ISBN 9780201380279

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Use a Maxwell relation from the previous problem and the third law of thermodynamics to prove that the thermal expansion coefficient $β$ (defined in Problem 1.7) must be zero at T=0.

Coefficient of Expansion becomes Zero at T=0.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Given Information

$M a x w e l l r e l a t i o n : {(\frac{\partial V}{\partial T})}_{P} = - {(\frac{δ S}{δ P})}_{T}$

Explanation

We know that " The thermal expansion coefficient is defined as the fractional change in volume per unit temperature change".

This means

$β = \frac{Δ V / V}{Δ T} β = \frac{1}{V} {(\frac{\partial V}{\partial T})}_{P}$

From the Maxwell relation $- {(\frac{δ S}{δ P})}_{T}$

So,

$β = \frac{1}{V} {(\frac{\partial V}{\partial T})}_{P} β = - \frac{1}{V} {(\frac{δ S}{δ P})}_{T}$

From the the third law of thermodynamics as $T \to 0$ , the entropy approaches to zero or some constant value which is independent of pressure.

This means ${(\frac{δ S}{δ P})}_{T}$ becomes Zero as $T \to 0 .$ and $β$ becomes 0.

We can conclude that coefficient of expansion becomes zero at $T \to 0 .$

Find Study Materials for

Create Study Materials

Select your language

An Introduction to Thermal Physics

Answers without the blur.

Short Answer

Use a Maxwell relation from the previous problem and the third law of thermodynamics to prove that the thermal expansion coefficient $β$ (defined in Problem 1.7) must be zero at T=0.

Step by Step Solution

Given Information

Explanation

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

An Introduction to Thermal Physics

Answers without the blur.

Short Answer

Use a Maxwell relation from the previous problem and the third law of thermodynamics to prove that the thermal expansion coefficient β (defined in Problem 1.7) must be zero at T=0.

Step by Step Solution

Given Information

Explanation

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Famous Physicists

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics

Use a Maxwell relation from the previous problem and the third law of thermodynamics to prove that the thermal expansion coefficient $β$ (defined in Problem 1.7) must be zero at T=0.