The problem with the data you're taking from literature is it's 1.12345 x T^5 (for example), so 1.12345 x 350^5Â if you do the sums how far off are you if you did the same with 1.234556 xT^5 ? Hence the use of piecewise linear tends to be safer. The error at a specific point will likely be far smaller than the rounding error multiplying a factor by 5,252,187,500,000 !Â
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