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
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,
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
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
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
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
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
to the enthalpy at 200 which is 2879.6, plus the fraction
of the temperature difference corresponds to the fraction of the enthalpy
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,
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
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
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
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
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
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
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
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
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
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
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.