Thermodynamics, Statistical Thermodynamics, & Kinetics
Thermodynamics, Statistical Thermodynamics, & Kinetics
3rd Edition
ISBN: 9780321766182
Author: Thomas Engel, Philip Reid
Publisher: Prentice Hall
Question
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Chapter 3, Problem 3.1CP
Interpretation Introduction

Interpretation:

The reason for the heat capacity Cp, mto be less than Cv, mfor H2O(l) which is nearly 40C needs to be determined.

Concept Introduction:

If the system experiences change from one thermodynamic phase to another due to change in properties such as temperature, volume, pressure, etc., then the system is said to have a thermodynamic process. Thermal capacity or heat capacityis the physical property of the matter.

Expert Solution & Answer
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Answer to Problem 3.1CP

Because of the change in the phase of water from solid to liquid at 40C.

Explanation of Solution

Generally, Cp, m is bigger than Cv, mand their difference is shown below:

  Cp,m- Cv,m= TVmβ2k..(1)

Here,

Cp, m= at constant pressure, molar heat capacity

  β = thermal expansion

Cv, m = at constant volume, molar heat capacity

Vm = molar volume

T = temperature

k = isothermal compressibility

The Cp, m >Cv, m if the right side of the equation (1) is positive. The thermal compressibility and thermal expansion are positive if there is no change in the phase of the system.

But in case of H2O (l) it is seen that Cp, m is smaller than Cv, m. but in case of water at 40C water is sometime in solid form because the melting point of ice is equal to the freezing point of water that is 00C. As here is a change in phase of water from solid to liquid at 40C the right side of the equation (1) becomes negative. The equation (1) can be rewritten as below:

Cp, m - Cv, m = -ve

Cp, m > Cv, m

Therefore, the heat capacity at constant volume is greater than the heat capacity at constant pressure of water at 40C.

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