Volumetric Thermal Expansion Coefft#

Using the definition

\[ß = \frac{1}{υ_s} \cdot \frac{δυ_s} {δT} = -\frac{1}{ρ_s} \cdot \frac{δρ_s} {δT} \tag{3}\]

and the density of water equation (2) the volumetric thermal expansion coefficient can be calculated with a simplified equation 0-150°C.

\[ß = a + b \cdot T + c \cdot T^{1.5} + d \cdot T^2\]

where

Var

Description

ß

is the coefft volumetric thermal expansion, 1/K

T

is temperature of the water °C

a

is -6.8785895e-05

b

is 2.1687942e-05

c

is -2.1236686e-06

d

is 7.7200882e-08

At the temperature of maximum density the coefficient of volumetric thermal expansion is zero as the values pass from positive to negative values.

Show/Hide Code 03vol_exp.py 
import altair as alt
import numpy as np
import pandas as pd

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

b = -6.8785895e-05 + 2.1687942e-05 * T - 2.1236686e-06 * np.power(T, 1.5) + \
    7.7200882e-08 * np.power(T,2)

source = pd.DataFrame({
  'Temperature °C': T,
  'Coefft Vol Thermal Expn 1/K': b
})

chart = alt.Chart(source).mark_line().encode(
    x=alt.X('Temperature °C', axis=alt.Axis(title='Temperature °C')),
    y=alt.Y('Coefft Vol Thermal Expn 1/K', axis=alt.Axis(title='Coefft Vol Thermal Expn 1/K')),
    tooltip=['Temperature °C', alt.Tooltip('Coefft Vol Thermal Expn 1/K', format='.5f')]
).properties(
        title={
            "text": "Coefficient Volumetric Thermal Expansion of Liquid Water"
        }
    )

chart.save('Vol_expn.html')

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