Type:

Other

Description:

Students in upper-level undergraduate thermodynamics courses were asked about the relationship between the complementary partial derivatives of the isothermal compressibility and the thermal expansivity of a substance. Both these material properties can be expressed with first partial derivatives of the system volume. Several of the responses implied difficulty with the notion of variables held fixed in a partial derivative. Specifically, when asked to find the partial derivative of one of these quantities with respect to a variable that was initially held fixed, a common response was that this (mixed second) partial derivative must be zero. We have previously reported other related difficulties in the context of the Maxwell relations, indicating persistent confusion applying partial differentiation to state functions. We present results from student homework and examination questions and briefly discuss an instructional strategy to address these issues.

Subjects:

  • Education > General
  • Mathematics > General

Education Levels:

  • Grade 1
  • Grade 6
  • Grade 8
  • Grade 9

Keywords:

NSDL,Education Foundations,thermal expansion,Life Science,Mathematics,Physics Education Research,General Physics,Graduate/Professional,partial derivatives,Thermal Properties of Matter,Mathematical Tools,Assessment,instructional strategy,Differential Equations,Higher Education,student difficulties,Undergraduate (Upper Division),Cognition,PERC 2006,partial differential equations,Learning Theory,oai:nsdl.org:2200/20071203141736503T,Physics,Thermo & Stat Mech,thermodynamic properties,NSDL_SetSpec_439869,Vocational/Professional Development Education,Education

Language:

English

Access Privileges:

Public - Available to anyone

License Deed:

Creative Commons Attribution Non-Commercial Share Alike

Collections:

None
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