At what point do the Kelvin and Celsius scales show the same numerical value?

The correct answer is that the Kelvin and Celsius scales do not show the same numerical value at any temperature above absolute zero. The Celsius and Kelvin scales are both temperature scales, but they are offset by 273.15 degrees. The Kelvin scale starts at absolute zero, which is 0 K, representing the lowest possible temperature where all molecular motion stops. In contrast, Celsius is based on the freezing point of water at 0 °C and its boiling point at 100 °C.

To find out when they show the same numerical value, one would set the Celsius temperature equal to the Kelvin temperature, recognizing the offset. This equation can be stated as follows: K = °C + 273.15. Since 273.15 is a fixed value added to the Celsius temperature to convert it to Kelvin, it is impossible for both scales to show the same numerical value except at absolute zero, where both can be interpreted conceptually as zero but not numerically equal in the common sense applied.

Thus, the Kelvin and Celsius scales will never show the same numerical value for any temperature above 0 K or -273.15 °C, reinforcing the understanding that they are independent scales differing by a constant offset across their ranges.