Unpacking the Meaning of Specific Heat Capacity in Base Units

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Discussion Overview

The discussion centers around the meaning and implications of expressing specific heat capacity in base units, specifically questioning the relevance and utility of the base unit representation (m2 s-2 K-1) in thermodynamics and related problems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant states that specific heat capacity is measured in joule per gram-kelvin (J g-1 K-1) and questions the meaning of its expression in base units (m2 s-2 K-1).
  • Another participant notes that using kilograms instead of grams makes the base unit equivalent but suggests that it is less intuitive for typical specific heat problems.
  • A participant seeks clarification on the significance of the base unit representation (m2 s-2 K-1) and its relation to specific heat capacity.
  • One participant proposes that while the base unit may not relate directly to typical thermodynamics problems, it could be useful in scenarios involving speed, providing an example where kinetic energy is converted into thermal energy and relates to temperature change.
  • A participant acknowledges the explanation provided by another participant.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of expressing specific heat capacity in base units, with some finding it less intuitive while others suggest it has specific applications. The discussion does not reach a consensus on the overall utility of the base unit representation.

Contextual Notes

The discussion highlights the potential limitations of using base units in practical thermodynamic problems and the assumptions involved in relating kinetic energy to thermal energy without resolving the mathematical steps fully.

mikkol
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specific heat capacity is measured in joule per gram-kelvin (J g–1 K–1). In base units it is m2 s-2 k-1.
Is that meaningless to express specific heat capacity in base units? Is there an explanation?

Thanks
Nick
 
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It's exactly equivalent if you replace the gram with kilogram, but fewer people would recognize it, and it's not as intuitive (because in specific heat problems you're usually given information in joules and kilograms, not meters).
 
ok, but what does exactly mean m2 s-2 k-1? What has it got to do with specific heat capacity?
 
It doesn't have much to do with typical thermodynamics problems, but it's well suited for a class of problems that involve speed. For example, if a homogeneous object with specific heat capacity c (in m2 s-2 K-1) is moving at a speed of x m s-1 and its kinetic energy is turned completely into thermal energy, then its temperature will increase by x2/2c kelvins. Independent of its mass! So there's a problem where your units might be more intuitive to use.

(Obviously I've just equated the original kinetic energy with the increase in thermal energy,

\frac{1}{2}mv^2=mc\Delta T

and canceled out the mass.)
 
thanks Mapes!
 

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