Estimate the fraction of unoccupied atomic sites in lead at temperature 10K below its melting point.
Vacancy fraction,nv/N temperature
1.8*10^-7 100C
7.2*10^-6 200C
express answer in vacancy fraction nv/N.
1*10^-4
To estimate the fraction of unoccupied atomic sites in lead at a temperature of 10K below its melting point, we can use the provided data on vacancy fraction at different temperatures.
From the given data, we can see that the vacancy fraction, nv/N, varies with temperature. However, we need to find the value at a temperature 10K below the melting point.
To estimate the value at this specific temperature, we need to perform linear interpolation between the two given data points.
Given Data:
Temperature T1 = 100°C
Vacancy fraction nv/N1 = 1.8 * 10^-7
Temperature T2 = 200°C
Vacancy fraction nv/N2 = 7.2 * 10^-6
Temperature T = Melting Point - 10K
Using linear interpolation formula:
nv/N = nv/N1 + (nv/N2 - nv/N1) * (T - T1) / (T2 - T1)
Let's calculate the fraction of unoccupied atomic sites in lead at temperature T = Melting Point - 10K.
First, convert the given temperatures to Kelvin:
T1 = 100°C + 273.15 = 373.15 K
T2 = 200°C + 273.15 = 473.15 K
Now, substitute the values into the formula:
nv/N = 1.8 * 10^-7 + (7.2 * 10^-6 - 1.8 * 10^-7) * (T - 373.15) / (473.15 - 373.15)
Simplifying the equation will give us the estimated fraction of unoccupied atomic sites in lead at the given temperature.