Question

Problem 1) In a certain crystalline material, the vacancy concentration at 45°C is twice that at 25°C. At what temperature would the vacancy concentration be one-half that at 25°C?

Answer 1

We use Boltzamm equation   N = exp ( -Q/RT)

where Q = energy required for vacancy formation

now ln ( N2/N1) = ( Q/R) ( 1/T1 -/T2)     is another form of above formula

T1 = 45C = 45+273 = 318 K , T2 = 25C = 298 K   we have N2 = 2N1

now ln ( 2)   = ( Q/8.314) ( 1/298 -1/318)

Q = 27305.427 J

now   T1 = 25C = 298 K , we were asked to fidn T2 where N2/N1 = 1/2 = 0.5

ln ( 0.5) = ( 27305.427 /8.314) ( 1/298 -1/T2)

T2 = 280.37 K = 280.37 - 273 C = 7.37 C