Question

It is expected that the data listed below between the vapour pressure p of water (in kPa) at different temperatures T (in K) will follow the relationship:

p= A.eB/T

where A and B are two constants which can be determined via curve fitting.

Estimate A and B based on the first two entries of the data below and calculate the error of using these values as a curve-fit for all the data.

Data:

Temperature (K)	Vapour Pressure (p)
2.7300000e+002	5.9995066e-001
2.7800000e+002	9.0659211e-001
2.8300000e+002	1.2132336e+000
2.8800000e+002	1.7331908e+000
2.9300000e+002	2.3198092e+000
2.9800000e+002	3.1997368e+000

Answer 1

T P 273 0.59995066 278 0.90659211 283 1.2132336 288 1.7331908 293 2.3198092 298 3.1997368 P = A e^B/T first part 0.59995066 = A e^B/273 ---(1) 0.90659211 = A e^B/278 ---(2) (2) divide (1) 1.511111113 = e^B/278 - B/273 1.511111113 = e^B (-6.588136 times 10^-5) 0.4128452 = B(-6.588136 times 10^-5) B = -0.062658506 times 10^5 = -6265.8506 Put B in (1) 0.59995066 = A e^-22.951833 A = 0.59995066 times 9286551401.99066 A = 5571472642.74 So P = 5571472642.74 e^-6265.8506/T for T P % error 283 1.3500079 11.27 288 1.9827790 14.40 293 2.8741862 23.89 298 4.1147615 27.54