# Specific heat in base units

1. Nov 17, 2008

### 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

2. Nov 17, 2008

### 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).

3. Nov 17, 2008

### mikkol

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

4. Nov 17, 2008

### 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 cancelled out the mass.)

5. Nov 17, 2008

### mikkol

thanks Mapes!