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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
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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:
Here,
Cp, m= at constant pressure, molar heat capacity
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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Chapter 3 Solutions
Thermodynamics, Statistical Thermodynamics, & Kinetics
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