# Is it 11% hotter today than it was yesterday?

Yesterday the temperature outside was 0.5 °C. Today, the temperature is 30 °C. 30 is 5300% more than 0.5, but today is obviously not 5300% hotter than yesterday.

In Fahrenheit, the temperatures are 33 °F and 86 °F, respectively. 160% hotter sounds more reasonable, but this argument uses the same logic as Celsius, just on a different scale.

Converting these temperatures to Kelvin, we get 273.70 K and 303.15 K, respectively. Since Kelvin is an absolute scale of temperature, can we correctly say that today is 11% hotter than yesterday?

Since temperature is relative, can we also claim that there is 11% more heat today?

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As you have proved, it depends on your reference point. All are correct. – ChrisF May 14 '13 at 21:22
@ChrisF I am not sure I have proven anything. I have shown relative differences in temperature, but am not sure how this translates logically to heat. – dlras2 May 14 '13 at 21:25
OK, "prove" is too strong. What you need to find out is what amount of energy 0.5 °C/33 °F/273.70 K represents and compare that to 30 °C/86 °F/303.15 K – ChrisF May 14 '13 at 21:27
@ChrisF Is that increase in energy 11% then? – dlras2 May 14 '13 at 21:32

@DanRasmussen It is. Multiply $T$ by $k/2$, where $k$ is the Boltzmann constant. This is then the heat energy per degree of freedom. For instance, if you have $N$ noninteracting point particles moving in 3 dimensions (3 translational d.o.f. and no internal ones), then you have internal energy $U = (3/2)NkT$, which is just what you learn is the case for a monatomic ideal gas. – Chris White May 14 '13 at 22:20