By what factor would the average kinetic energy of the particles by increased if the temperature of a substance was increased from - 49°C to 287°C?

Average kinetic energy of a particle:

0.5 mv^2 = kT/2

so the kinetic energy = kT/2

assuming the same value of K

T1 = - 49 + 273 = 224

T2 = 287 + 273 = 560

E2 / E1 = kT2 / 2 / kT1 / 2

E2 / E1 = T2 / T1

E2 / E1 = 560 / 224 = 2.5

so the average kinetic energy of the particle increases by 2.5