File:Air density vs temperature.svg

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Original file ‎(SVG file, nominally 575 × 431 pixels, file size: 51 KB)

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English: Air density vs. Temperature graph with exponential and 2nd-order polynomial trends. Data from w:en:Density#Air
Date
Source Own work
Author T.seppelt
SVG development
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This plot was created with Matplotlib.
Source code
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Python code

import csv, numpy,scipy,scipy.optimize
import matplotlib.pyplot as plt
x = []
y = []
with open("data.csv", "r") as f:
    for line in csv.DictReader(f, fieldnames=['x','y'], delimiter=';'):
        x.append(int(line['x']))
        y.append(float(line['y']))
x = numpy.array(x)
y = numpy.array(y)

intx = numpy.linspace(min(x), max(x), 100)
P1 = numpy.poly1d(numpy.polyfit(x, y, 2))

P2_data = scipy.optimize.curve_fit(lambda t,a,b: a*numpy.exp(b*t),  x,  y, )[0]
P2 = lambda x : P2_data[0]*numpy.exp(P2_data[1]*x)

plt.scatter(x,y, label="Density of air at 1 atm pressure")
plt.plot(intx, P1(intx), label = "Polynomial Trend\n$x \mapsto 10^{{-5}} x^2 {}x+{}$".format(*numpy.round(P1,4)[1:]))
plt.plot(intx, P2(intx), label = "Exponential Trend\n$x \mapsto \exp({}x) {} $".format(* numpy.round(P2_data,4)))
plt.legend()
plt.xlabel("Temperature [°C]")
plt.ylabel("Density [kg/m³]")
plt.title("Air density vs. temperature")
plt.savefig("output.svg",format="svg",transparent=True)

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
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Under the following conditions:
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Date/TimeThumbnailDimensionsUserComment
current11:09, 5 October 2017Thumbnail for version as of 11:09, 5 October 2017575 × 431 (51 KB)T.seppelt (talk | contribs)exp as function without exponent
07:55, 4 October 2017Thumbnail for version as of 07:55, 4 October 2017575 × 431 (51 KB)T.seppelt (talk | contribs)User created page with UploadWizard

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