SME
Engineering Thermodynamics · Problem type
Linear interpolation in a property table
Use this for “Superheated steam at 400 kPa has h = 2861 kJ/kg at 200 °C and 2965 kJ/kg at 250 °C. Estimate h at 220 °C.”
Chart
h(225) = 2,908
Ringed: the nodes (200, 2,855), (250, 2,961)
This is an example. Type your own values to start a new problem.
h (kJ/kg)
=
h₁ (kJ/kg)
+
(
T (°C)
−
T₁ (°C)
)
×
(
h₂ (kJ/kg)
−
h₁ (kJ/kg)
)
÷
(
T₂ (°C)
−
T₁ (°C)
)
Formulas
h
=
h₁
+
(
T
−
T₁
)
×
h₂
−
h₁
T₂
−
T₁
2,908
=
2,855
+
(225
−
200)
×
2,961 − 2,855
250 − 200
Assumptions
•
Between two neighboring table rows, h changes along a straight line with T.
•
Read both rows at the same pressure; T lies between T₁ and T₂.
•
The same steps interpolate any property (v, u, s) against T or P.
Step-by-step
WE KNOW
T = 225 °C, T₁ = 200 °C, h₁ = 2,855 kJ/kg, T₂ = 250 °C, h₂ = 2,961 kJ/kg
FIND
enthalpy (h)
Step 1 · Find enthalpy (h)
Use h = h₁ + (T − T₁) × (h₂ − h₁) ÷ (T₂ − T₁)
Go
the
share
T
−
T₁
T₂
−
T₁
of
the
way
from
h₁
to
h₂
along
the
line.
h
=
2,855
+
(225
−
200)
×
2,961 − 2,855
250 − 200
h
=
2,855
+
25
×
106
50
h
=
2,855
+
2,650
50
h
=
2,855
+
53
h
=
2,908
kJ/kg
Check
Put the numbers back in. Both sides should match.
2,908
=
2,855
+
(225
−
200)
×
2,961 − 2,855
250 − 200
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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