Temperature Gradient: Explained in Thermodynamics

[Benny]

Hi, can someone please explain to me what is meant by a temperature gradient in the context of thermodynamics? Something I've been reading goes along the lines of "...To reverse the direction of conduction would require a reversal of the temperature gradient in the conductor. Thermal conduction is clearly irreversible, but the energy is already thermal and cannot be converted into heat.."

I've seen the word gradient used in a few different contexts, I'm just wondering what it means in this case. Any help would be good thanks.

 

[Hootenanny]

The thermal gradient is the rate of change of temperature with respect to distance.

 

[siddharth]

The temperature gradient is
$$\nabla T$$
In cartesian coordinates
$$\nabla T = \left( \frac{\partial T}{\partial x}, \frac{\partial T}{\partial y}, \frac{\partial T}{\partial z} \right)$$
It tells you the rate and direction at which the temperature changes most rapdily in a particular region.

 

[Benny]

Thanks for the responses guys.