Volumetric Temperature Expansion

Overview

Engineering reference data for Volumetric Temperature Expansion in thermodynamics.

Key Formulas

First Law

$\Delta U = Q - W$

Energy is conserved — heat added minus work done.

Ideal Gas Law

$PV = nRT$

Relates pressure, volume, and temperature of an ideal gas.

Heat Transfer

$Q = mc\Delta T$

Sensible heat transfer.

Carnot Efficiency

$\eta = 1 - T_C/T_H$

Maximum efficiency between two temperatures.

Variables

Symbol	Description	Unit
$U$	Internal energy	J
$Q$	Heat	J
$W$	Work	J
$P$	Pressure	Pa
$V$	Volume	m³
$T$	Temperature	K

Volumetric Temperature Coefficients for Water

Water exhibits unique volumetric expansion behavior due to its density maximum at 4°C. The expansion coefficient (β) varies significantly with temperature, especially below 10°C. The following table provides accurate coefficients for common temperature ranges.

Note: To calculate an average coefficient over a temperature range where β varies significantly (e.g., 20-40°C for water), it is often necessary to interpolate or average the values from the table. For the range 20-40°C, the average β is approximately:

$$\beta_{avg} = \frac{0.000207 + 0.000303 + 0.000385}{3} = 0.000298 \ \text{1/°C}$$

Practical Examples

Example 1: Metric Units - Heating Oil

Given: 100 liters (0.1 m³) of oil, $\beta = 0.00070 \ \text{1/°C}$, heated from 20°C to 40°C. Calculation:

$$dV = V_0 \cdot \beta \cdot (t_1 - t_0) = (0.1 \ \text{m}^3) \cdot (0.00070 \ \text{1/°C}) \cdot (40 - 20) = 0.0014 \ \text{m}^3$$

Result: Expansion volume = 1.4 liters. Final volume = 101.4 liters.

Example 2: Imperial Units - Heating Oil

Given: 30 U.S. gallons of oil, $\beta = 0.00039 \ \text{1/°F}$, heated from 70°F to 100°F. Calculation:

$$dV = V_0 \cdot \beta \cdot (t_1 - t_0) = (30 \ \text{gal}) \cdot (0.00039 \ \text{1/°F}) \cdot (100 - 70) = 0.351 \ \text{gal}$$

Result: Expansion volume = 0.351 gallons. Final volume = 30.351 gallons.

Interactive Charts

References

• Original Source