Temperature Physics Example 4

Solution

1. 1
   On the Kelvin scale, temperature is proportional to average kinetic energy of particles: $KE_{\text{avg}} = \frac{3}{2}k_B T$.
2. 2
   At $400 \text{ K}$, the average KE is indeed twice that at $200 \text{ K}$, so in terms of thermal energy, the statement is correct.
3. 3
   However, converting to Celsius: $200 \text{ K} = -73°\text{C}$ and $400 \text{ K} = 127°\text{C}$. In Celsius, $127$ is not twice $-73$, showing that 'twice as hot' only makes physical sense on an absolute (Kelvin) scale.