Why is it incorrect to say that a gas sample of helium at 50 degree Celsius is twice as hot as a sample of helium at 25 degree Celsius? Describe your answer using words, math, and/or pictures.

Answer 1

What matters is the absolute temperature, i.e. the Kelvin scale, of the substance. Recall that the conversion of Celsius to Kelvin and vice versa is:

T(K) = T(^oC) + 273 K [Celsius to Kelvin]

T(^oC) = T(K) - 273 K [Kelvin to Celsius]

In the current case a gas at 25 ^oC represents a temperature of 298 K and at 50 ^oC represents a temperature of 323 K. This only represents an increase in Kelvin temperature of only 8.4%.

A substance at 298 K (25 ^oC) would need to be heated to 596 K, or 323 ^oC, to be twice as "hot."

Hope this helps!