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Q. 2.13

An Introduction to Thermal Physics
Found in: Page 62
An Introduction to Thermal Physics

An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

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Short Answer

Fun with logarithms.
a Simplify the expression ealnb. (That is, write it in a way that doesn't involve logarithms.)b Assuming that b <<a, prove that ln(a+b)(lna)+(b/a). (Hint: Factor out the afrom the argument of the logarithm, so that you can apply the approximation of part d of the previous problem.)

Part a

aThe expressions is ealn(b)=ba.

Part b

bThe equation ln(a+b)ln(a)+bais proved.

See the step by step solution

Step by Step Solution

Step: 1 Simplify steps: (part a)

We know that,


The logarithm rule is


Step: 2  Equating part: (part b)

Consider b<<aand factor a as


Using Taylor formula as


Step: 3 Proving part: (part b)

We have,

ln(1+x) at x0=0 as,


Hence,the equation is proved.

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