It is sometimes said that kBT at room temperature is about 1

It is sometimes said that kBT at room temperature is about 140eV. For what temperature T would this be exactly correct? By about what percent is this off at T = 298 K?

Solution

Here,   kBT   =   (1/40) * 1.6 * 10^-19

Here, boltzmann constant , kB = 1.3806 × 10^-23 m² kg s^-2 K^-1

=>   1.3806 × 10^-23 * T = (1/40) * 1.6 * 10^-19

=> T   =    289.729 K temperature T would this be exactly correct

=> percent error   = (298 - 289.729)/(298)   * 100

                               =   2.775 %