Find by double iterpolation the entropy of steam at 297 psia

Find by double iterpolation the entropy of steam at 297 psia and 512 F using the table in the text book used in this course, borgnakke & sontag, fundamentals of thermodynamics.

Solution

Entropy of steam at nearest temperature and pressure:

Interpolation formula:

y_t = y₁ + (y₂ - y₁) * (x_t - x₁)/(x₂ - x₁)

for double interpolation we have to use interpolation formula thrice.

First by using interpolation get entropy at 200 psia and 512 F:

y_t1 = 1.6239 + (1.6512-1.6239) * ((512-500)/(600-550)) = 1.6303

Similarly by using interpolation get entropy at 300 psia and 512 F:

y_t2 = 1.5701 +(1.5997-1.5701) * ((512-500)/(550-500)) = 1.5772

Now by using interpolation get entropy at 297 psia and 512 F:

y_t2 = 1.6303 + (1.5767-1.6303) * ((297-200)/(300-200)) = 1.5787

So the entropy of steam at 512 F and 297 psia is 1.5787 Btu/lbm R.

	500 F	550 F
200 psia	1.6238	1.6512
300 psia	1.5701	1.5997