Many times, the state of a system does not fall exactly at a value reported in Steam Tables. This is when interpolation is required between the two adjacent properties on a given table. Let us assume that the properties φ1 and φ2 are given at temperatures T1 and T2, respectively. To determine the value of φ at any temperature between T1 and T2, we assume a linear variation of φ with respect to temperature between T1 and T2 as shown in the graph below:
By integrating the slope
of the interpolation line we can develop an expression for our interpolation as
shown below:
Example:
Calculate the Internal Heat Energy (U) of a substance at 237°C and 800 kPa.
Given that for this substance at 800 kPa at 200°C, U = 2630.6 kJ/kg and at
250°C, U = 2715.5 kJ/kg.
Assuming a linear
variation of U from 200 to 250°C, the change in U with respect to temperature
is:
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