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Chapter 5: Q. 5.13 (page 159)

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

Short Answer

Expert verified

Coefficient of Expansion becomes Zero at T=0.

Step by step solution

01

Given Information

Maxwell relation: ∂V∂TP=-δSδPT

02

Explanation

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

β=ΔV/VΔTβ=1V∂V∂TP

From the Maxwell relation we have-δSδPT

SO,

β=1V∂V∂TPβ=-1VδSδPT

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

This means δSδPTbecomes Zero as T→0 and βbecomes 0 as T→0.


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Most popular questions from this chapter

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