Would it be possible to have a temperature scale defined in such a way that the hotter an object or system got, the lower (less positive or more negative) its temperature was?

Temperature is a measure of the average kinetic energy of particles in a substance. The hotter an object or system gets, the higher its average kinetic energy. In most temperature scales, like Celsius and Fahrenheit, temperature increases with the increase in average kinetic energy.

In order to create a temperature scale where the temperature decreases as the object gets hotter, we would need to invert the relationship between temperature and kinetic energy. One way to do this is to define the new temperature scale as inversely proportional to the average kinetic energy of particles.

Let's call this new temperature scale "Reverse Temperature (R)". We can define it as: R = -k * T Where 'k' is a constant of proportionality and 'T' is the temperature measured in a typical scale like Kelvin (since Kelvin's scale starts from 0, it would be useful for this case). When the average kinetic energy (and thus T) increases, the R-value will decrease.

This new reverse temperature scale satisfies the condition in the exercise - it is inversely proportional to the heat of an object or system, meaning the temperature value would decrease as the object or system got hotter. However, it is essential to consider the practicality of implementing such a scale. In some niche applications, it might serve as a useful tool. Yet, it would be quite counterintuitive for everyday use compared to current temperature scales like Celsius, Kelvin, or Fahrenheit. In conclusion, while it is technically possible to have a temperature scale that decreases as an object or system gets hotter, it may not be practical for widespread use. However, it could have potential use in some specific scientific applications.