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Related Concept Videos

SI Units: 2019 Redefinition01:13

SI Units: 2019 Redefinition

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Measurement is an indispensable part of analytical chemistry. The result of measurement helps quantify a substance's physical property and compare it with the physical property of another substance. Each measurement comprises two components - a number indicating the magnitude and a unit of measurement as a standard for comparison. Further, the same quantity can be measured using different units of measurement, which leads to differences in magnitude.
A standard set of units has been defined...
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The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
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Numerical Calculations01:24

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In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
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Measurement: Standard Units03:38

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Every measurement provides three kinds of information: the size or magnitude of the measurement (a number), a standard of comparison for the measurement (a unit), and an indication of the uncertainty of the measurement. While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the errors in the measurement results.
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Uncertainty in Measurement: Significant Figures03:34

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All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.
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Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
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Can C Be Less Than C ?

Yingbin Ge1, Samuel L Montgomery1, Gabriel L Borrello1

  • 1Department of Chemistry, Central Washington University, Ellensburg, Washington 98926, United States.

ACS Omega
|May 31, 2021
PubMed
Summary

The specific heat capacities at constant pressure (Cp) and constant volume (Cv) are fundamentally equal. Even for substances like water that contract when heated, Cp cannot be less than Cv due to internal pressure considerations.

Area of Science:

  • Thermodynamics
  • Physical Chemistry
  • Chemical Engineering

Background:

  • A common misconception in thermodynamics suggests that specific heat capacity at constant pressure (Cp) can be less than specific heat capacity at constant volume (Cv).
  • This misconception often arises from observing anomalous thermal expansion, such as water contracting when heated between 0 and 4 °C.
  • Textbooks sometimes present flawed reasoning that leads students to believe Cp < Cv under such conditions.

Purpose of the Study:

  • To fundamentally address the question of whether Cp can be less than Cv.
  • To correct the misconception that anomalous thermal expansion implies Cp < Cv.
  • To clarify the role of internal energy and internal pressure in the relationship between Cp and Cv.

Main Methods:

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  • Thermodynamic analysis considering the internal energy variation with volume (internal pressure).
  • Application of the Clausius inequality.
  • Re-evaluation of heat capacity definitions under isobaric and isochoric conditions.

    • Main Results:

    • The assumption that internal energy change depends solely on temperature change is fundamentally flawed.
    • Neglecting the contribution of internal pressure to internal energy changes leads to incorrect conclusions about heat capacities.
    • When internal pressure is correctly accounted for, it is demonstrated that Cp cannot be less than Cv for any substance.

    Conclusions:

    • The relationship Cp ≥ Cv holds true for all substances under all conditions.
    • Anomalous thermal expansion does not lead to a violation of fundamental thermodynamic principles regarding heat capacities.
    • A correct understanding of internal energy requires accounting for both temperature and volume dependencies.