Superficial Thermal Expansion

Overview

Engineering reference data for Superficial Thermal 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

Superficial Expansion Formula

The fundamental formula for calculating the change in area due to temperature change:

$dA = A_0 \gamma (t_1 - t_0)$

Where:

• $dA$ = change in area (m²)
• $A_0$ = initial area (m²)
• $\gamma$ = superficial expansion coefficient (m²/m²·K)
• $t_0$ = initial temperature (°C)
• $t_1$ = final temperature (°C)

Relationship to Linear Expansion

The superficial (area) expansion coefficient can be approximated from the linear expansion coefficient:

$\gamma \approx 2\alpha$

Where $\alpha$ is the linear temperature expansion coefficient (m/m·°C).

Common Material Coefficients

Linear temperature coefficients ($\alpha$) for commonly used engineering metals:

References

• Original Source