%0 Journal Article %1 thompson:85 %A Thompson, John R. %A Manogue, Corinne A. %A Roundy, David J. %A Mountcastle, Donald B. %D 2012 %E Rebello, N. Sanjay %E Engelhardt, Paula V. %E Singh, Chandralekha %I AIP %J AIP Conference Proceedings %K 2012 education mathematics properties thermodynamic %N 1 %P 85-88 %R 10.1063/1.3680000 %T Representations of partial derivatives in thermodynamics %U http://dx.doi.org/10.1063/1.3680000 %V 1413 %X One of the mathematical objects that students become familiar with in thermodynamics, often for the first time, is the partial derivative of a multivariable function. The symbolic representation of a partial derivative and related quantities present difficulties for students in both mathematical and physical contexts, most notably what it means to keep one or more variables fixed while taking the derivative with respect to a different variable. Material properties are themselves written as partial derivatives of various state functions (e.g., compressibility is a partial derivative of volume with respect to pressure). Research in courses at the University of Maine and Oregon State University yields findings related to the many ways that partial derivatives can be represented and interpreted in thermodynamics. Research has informed curricular development that elicits many of the difficulties using different representations (e.g., geometric) and different contexts (e.g., connecting partial derivatives to specific experiments).

@article{thompson:85, abstract = {One of the mathematical objects that students become familiar with in thermodynamics, often for the first time, is the partial derivative of a multivariable function. The symbolic representation of a partial derivative and related quantities present difficulties for students in both mathematical and physical contexts, most notably what it means to keep one or more variables fixed while taking the derivative with respect to a different variable. Material properties are themselves written as partial derivatives of various state functions (e.g., compressibility is a partial derivative of volume with respect to pressure). Research in courses at the University of Maine and Oregon State University yields findings related to the many ways that partial derivatives can be represented and interpreted in thermodynamics. Research has informed curricular development that elicits many of the difficulties using different representations (e.g., geometric) and different contexts (e.g., connecting partial derivatives to specific experiments).}, added-at = {2012-05-09T10:07:29.000+0200}, author = {Thompson, John R. and Manogue, Corinne A. and Roundy, David J. and Mountcastle, Donald B.}, biburl = {https://www.bibsonomy.org/bibtex/2cca7cae3bddb170a9610c2b9fa6c559c/thorade}, description = {Representations of partial derivatives in thermodynamics | Browse - AIP Conference Proceedings}, doi = {10.1063/1.3680000}, editor = {Rebello, N. Sanjay and Engelhardt, Paula V. and Singh, Chandralekha}, interhash = {a3be5953f5e4298c96f5a63c72abe38b}, intrahash = {cca7cae3bddb170a9610c2b9fa6c559c}, journal = {AIP Conference Proceedings}, keywords = {2012 education mathematics properties thermodynamic}, number = 1, pages = {85-88}, publisher = {AIP}, timestamp = {2012-05-09T10:07:29.000+0200}, title = {Representations of partial derivatives in thermodynamics}, url = {http://dx.doi.org/10.1063/1.3680000}, volume = 1413, year = 2012 }