The table below shows the density of air at 1 atm at different temperatures: a.

Question

The table below shows the density of air at 1 atm at different temperatures: a. Estimate the density at 5 degree C using linear interpolation. b. The value reported by the table was 1.269 kg/m^3. What is the percentage error in the linear interpolation value? Assuming there is a linear relationship between temperature and density, use the data at 0 degree C and 10 degree C from the table. You can find the equation of the straight line that goes through points A and B, and then find the y coordinate of point C:

Explanation / Answer

a. By linear interpolation,

(y - y0) / ( x - x0 ) = (y1 - y0)/ (x1 -x0)

y = y0 + (x - x0) (y1 -y0)/ (x1 -x0)

x0 = 0, y0 = 1.293

x1 = 10, y0 = 1.247

y = 1.293 + (5 - 0) * (1.247 - 1.293) / (10 -0)

y = 1.27 kg/m3

b. Reported value = 1.269 kg/m3

Percent error in linear interpolation = l1.269 - 1.27l/ 1.269 * 100 = 0.079 %

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