Liquid Density#

Liquid density has a simplified equation valid in the temperature range 0 to 150°C. Once again the range is shown only for 0 to 30°C.

\[ρ_s = a + b\cdot T + c\cdot T^2 +d\cdot T^{2.5} + e\cdot T^3 \tag{2}\]

where

Var

Description

ρs

is the density of liquid water, kg/m³

T

is temperature of the water °C

a

is 999.79684

b

is 0.068317355

c

is -0.010740248

d

is 0.00082140905

e

is -2.3030988e-05

The plot shows the maximum at the point of maximum density.

Show/Hide Code 02density_water.py 
import altair as alt
import numpy as np
import pandas as pd

T = np.linspace(0, 30, 31)

ps = 999.79684 + 0.068317355 * T - 0.010740248 * np.power(T, 2) \
    + 0.00082140905 * np.power(T, 2.5) - 2.3030988e-05 * np.power(T, 3)

source = pd.DataFrame({
  'Temperature °C': T,
  'ρs kg/m³': ps
})

chart = alt.Chart(source).mark_line().encode(
    x='Temperature °C',
    y=alt.Y('ρs kg/m³',
        scale=alt.Scale(domain=(995, 1000)),
        axis=alt.Axis(title='Density kg/m³')
        ),
    tooltip=['Temperature °C', alt.Tooltip('ρs kg/m³', format='.3f')]
).properties(
        title={
            "text": "Density of Liquid Water",
            "color": "red"
        }
    )

chart.save('Density_water_title_red.html')

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