In newton's law of cooling in the form
`(dDeltatheta)/(dt)=-kDeltatheta`
What factors does the constant k depend upon? What are the dimensions of k?

Explanation

To solve the question regarding Newton's law of cooling, we will break it down into two parts: identifying the factors that the constant \( k \) depends upon, and determining the dimensions of \( k \).

### Step 1: Factors that \( k \) Depends Upon
1. **Shape of the Material**: The geometry of the object affects how heat is distributed and lost. Different shapes will have different surface areas and volumes, which influence the rate of cooling.

2. **Type of Material**: Different materials have varying thermal conductivities. For example, metals generally lose heat faster than insulators due to their higher thermal conductivity.

3. **Surface Characteristics**: The roughness or smoothness of the surface can impact the heat transfer rate. A rough surface may trap air and create insulating layers, while a smooth surface may allow for better heat dissipation.
...