Unpacking the Meaning of Specific Heat Capacity in Base Units

[mikkol]

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

 

[Mapes]

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).

 

[mikkol]

ok, but what does exactly mean m² s^-2 k^-1? What has it got to do with specific heat capacity?

 

[Mapes]

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.)

 

[mikkol]

thanks Mapes!