Here we're going to look at using interpolation to get values in the steam tables when the
Here we're going to look at using interpolation to get values in the steam tables when the

steam tables are not detailed enough to list the values that we're interested in. So in
steam tables are not detailed enough to list the values that we're interested in. So in

this case we have water at 220 degrees centigrade, 0.0100 MPa
this case we have water at 220 degrees centigrade, 0.0100 MPa

and we want to know what's the enthalpy. So if we go to the steam tables,
and we want to know what's the enthalpy. So if we go to the steam tables,

look up the saturation temperature at this pressure its only 45.8 degrees
look up the saturation temperature at this pressure its only 45.8 degrees

centigrade which means at this temperature we're well above saturation so what we have
centigrade which means at this temperature we're well above saturation so what we have

is superheated steam and so now we can go to the superheated steam tables and we can
is superheated steam and so now we can go to the superheated steam tables and we can

look up values but the tables I'm going to use, and these are from Elliott and Lira the
look up values but the tables I'm going to use, and these are from Elliott and Lira the

thermodynamics textbook but you can find steam tables in a number of locations, don't list
thermodynamics textbook but you can find steam tables in a number of locations, don't list

values at 220 degrees C, what I can find is at 200 degrees
values at 220 degrees C, what I can find is at 200 degrees

C and at 250 degrees C I can find the enthalpy at a pressure of
C and at 250 degrees C I can find the enthalpy at a pressure of

0.01 MPa so let me write those values down however I want a value at
0.01 MPa so let me write those values down however I want a value at

220 degrees C so let me call that just H for now and I'm going to
220 degrees C so let me call that just H for now and I'm going to

get that by interpolating, what we're going to say is the enthalpy at 220 is equal
get that by interpolating, what we're going to say is the enthalpy at 220 is equal

to the enthalpy at 200 which is 2879.6, plus the fraction
to the enthalpy at 200 which is 2879.6, plus the fraction

of the temperature difference corresponds to the fraction of the enthalpy
of the temperature difference corresponds to the fraction of the enthalpy

difference, in other words 220 minus 200 over 250 minus 200,
difference, in other words 220 minus 200 over 250 minus 200,

and if I multiply that by the enthalpy difference in that range, and I'll do the calculation,
and if I multiply that by the enthalpy difference in that range, and I'll do the calculation,

enthalpy is 2918.7, we can't really justify that many significant
enthalpy is 2918.7, we can't really justify that many significant

figures so I'm going to write it as 2920 kJ/kg that we
figures so I'm going to write it as 2920 kJ/kg that we

get by interpolation. Now I'm going to do a similar problem, the difference here is
get by interpolation. Now I'm going to do a similar problem, the difference here is

I want enthalpy at a higher pressure, we're still in the superheated region of the steam
I want enthalpy at a higher pressure, we're still in the superheated region of the steam

tables but this pressure is also not listed in the steam tables. I'm going to use the
tables but this pressure is also not listed in the steam tables. I'm going to use the

data in the calculations from part one, so let me list them first. So I've listed the
data in the calculations from part one, so let me list them first. So I've listed the

values that we calculated and what we looked up in the previous and then we don't have
values that we calculated and what we looked up in the previous and then we don't have

values at 0.02 MPa in the table but we have them at
values at 0.02 MPa in the table but we have them at

0.05 MPa, let me write those values down. So what we're going to do is
0.05 MPa, let me write those values down. So what we're going to do is

first calculate H2 by interpolation doing the exact same procedure we did in the first
first calculate H2 by interpolation doing the exact same procedure we did in the first

problem and then we're going to interpolate in pressure to get H3 so H2 I'm going to just
problem and then we're going to interpolate in pressure to get H3 so H2 I'm going to just

write the numbers down and not discuss them since its identical to what we just finished
write the numbers down and not discuss them since its identical to what we just finished

doing and end up with a value of 2917.1 and so now I can interpolate
doing and end up with a value of 2917.1 and so now I can interpolate

between this value and this value, of course it's not a very strong dependence on pressure
between this value and this value, of course it's not a very strong dependence on pressure

for a gas at low pressure but we'll do the calculation just to demonstrate the idea when
for a gas at low pressure but we'll do the calculation just to demonstrate the idea when

we have to do these multiple interpolations. So what we're going to do is calculate H3
we have to do these multiple interpolations. So what we're going to do is calculate H3

as being the value at 220 and the lower pressure plus again the difference,
as being the value at 220 and the lower pressure plus again the difference,

0.02 but now in pressure over a range that we have values and the difference in
0.02 but now in pressure over a range that we have values and the difference in

enthalpy and I'll do the math for this calculation and so we now have the value for H3 now in
enthalpy and I'll do the math for this calculation and so we now have the value for H3 now in

terms of significant figures it's essentially, we're going to say it's the same number, because
terms of significant figures it's essentially, we're going to say it's the same number, because

of that weak dependence on pressure and we don't have accurate enough values, so in three
of that weak dependence on pressure and we don't have accurate enough values, so in three

significant figures 2920 kJ/kg at this higher pressure.
significant figures 2920 kJ/kg at this higher pressure.