Influence of uncertainties and assessment of significant digits in thermodynamics

Randall D. Manteufel; Amir Karimi

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Conference: 2013 ASEE Annual Conference & Exposition
Location: Atlanta, Georgia
Publication Date: June 23, 2013
Start Date: June 23, 2013
End Date: June 26, 2013
ISSN: 2153-5965
Conference Session: Mechanical Engineering (ME) Poster Session
Tagged Division: Mechanical Engineering
Page Count: 18
Page Numbers: 23.746.1 - 23.746.18
DOI: 10.18260/1-2--19760
Permanent URL: https://peer.asee.org/19760
Download Count: 406

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Randall D. Manteufel University of Texas, San Antonio

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Dr. Randall Manteufel is an associate professor in Mechanical Engineering at the University of Texas at San Antonio. He teaches courses in thermodynamics, fluid mechanics and heat transfer. He is the faculty advisor for the student chapter of American Society for Heating Refrigerating and Air-Conditioning Engineers at UTSA.

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Amir Karimi University of Texas, San Antonio

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Abstract

Influence of uncertainties and assessment of significant digits in thermodynamics Engineering thermodynamics calculations are predominately deterministic where students are expected to solve a problem for quantities which can be calculated to many significant digits using a calculator or software program. Students often report final answers to many more significant digits than justifiable. Many foundational textbooks in physics, chemistry, statics, and measurements stress that final answers are justifiable to a limited number of digits because of the lack of precision of inputs and/or internal coefficients/models. It is often recommend that final results be expressed to three significant digits. Students are encouraged to keep intermediate digits in multi‐step calculations and then round the final result to the appropriate number of significant digits. It has been observed that the appropriate number of significant digits continues to be a difficult concept for many students. Some have the misconception that an answer with five or six significant digits is equivalent to, if not better than, an answer with fewer digits. Having struggled with teaching this concept, it was decided to require calculations with uncertain inputs in a class where it is not typically covered. In engineering thermodynamics textbooks, typical problems have input values which no specified uncertainty. For example, the inlet temperature may be specified to be 480°C or the pressure to be 2.0 MPa. A number of thermodynamic examples and homework problems have been developed that include uncertainties which must be propagated. Both hand calculations are demonstrated followed by implementation in a spreadsheet program which allows the student to access routines to evaluate thermodynamic properties. The approach is based on the traditional differential method for uncertainty propagation yet numerical differentiation in used in the spreadsheet program. The approach is general such that uncertainties can be specified for a large range of inputs such as: temperatures, pressures, mass flow rates, component isentropic efficiencies, etc. Examples show that when seemingly inconsequential uncertainties are considered, there can be relatively large percent uncertainties in both intermediate and final results such as: thermal efficiency, back work ratio, and turbine power. Both pre and post‐assessments were conducted to gauge the effect of the new problems on student learning and attitudes. Students show an increased perception of the significant of properly reporting answers to an appropriate number of significant digits, and a positive attitude toward the methods covered. Some student comments indicate that the methods were inadequately covered in prerequisite classes. This is useful information for continuous improvement of the engineering curriculum. Students also anticipate using the methods demonstrated in the thermodynamics class in subsequent engineering classes, indicating a deeper understanding of uncertainties and significant digits.

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Manteufel, R. D., & Karimi, A. (2013, June), Influence of uncertainties and assessment of significant digits in thermodynamics Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--19760

TY  - CPAPER
AB  - Influence of uncertainties and assessment of significant digits in thermodynamics    Engineering thermodynamics calculations are predominately deterministic where students are expected to solve a problem for quantities which can be calculated to many significant digits using a calculator or software program.  Students often report final answers to many more significant digits than justifiable.  Many foundational textbooks in physics, chemistry, statics, and measurements stress that final answers are justifiable to a limited number of digits because of the lack of precision of inputs and/or internal coefficients/models.  It is often recommend that final results be expressed to three significant digits.  Students are encouraged to keep intermediate digits in multi‐step calculations and then round the final result to the appropriate number of significant digits.  It has been observed that the appropriate number of significant digits continues to be a difficult concept for many students.  Some have the misconception that an answer with five or six significant digits is equivalent to, if not better than, an answer with fewer digits.  Having struggled with teaching this concept, it was decided to require calculations with uncertain inputs in a class where it is not typically covered.  In engineering thermodynamics textbooks, typical problems have input values which no specified uncertainty.  For example, the inlet temperature may be specified to be 480°C or the pressure to be 2.0 MPa.   A number of thermodynamic examples and homework problems have been developed that include uncertainties which must be propagated.  Both hand calculations are demonstrated followed by implementation in a spreadsheet program which allows the student to access routines to evaluate thermodynamic properties.  The approach is based on the traditional differential method for uncertainty propagation yet numerical differentiation in used in the spreadsheet program.  The approach is general such that uncertainties can be specified for a large range of inputs such as: temperatures, pressures, mass flow rates, component isentropic efficiencies, etc.  Examples show that when seemingly inconsequential uncertainties are considered, there can be relatively large percent uncertainties in both intermediate and final results such as: thermal efficiency, back work ratio, and turbine power.  Both pre and post‐assessments were conducted to gauge the effect of the new problems on student learning and attitudes.  Students show an increased perception of the significant of properly reporting answers to an appropriate number of significant digits, and a positive attitude toward the methods covered.  Some student comments indicate that the methods were inadequately covered in prerequisite classes.  This is useful information for continuous improvement of the engineering curriculum.  Students also anticipate using the methods demonstrated in the thermodynamics class in subsequent engineering classes, indicating a deeper understanding of uncertainties and significant digits.  
AU  - Randall D. Manteufel
AU  - Amir Karimi
CY  - Atlanta, Georgia
DA  - 2013/06/23
PB  - ASEE Conferences
TI  - Influence of uncertainties and assessment of significant digits in thermodynamics
UR  - https://peer.asee.org/19760
DO  - 10.18260/1-2--19760
ER  -