Thin Circular Ring Radius Temperature Change

Overview

Engineering reference data for Thin Circular Ring Radius Temperature Change 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

Example: Steel Pipe Diameter Temperature Expansion

A stainless steel pipe with nominal diameter 10 inches (outside diameter 10.750 inches) is heated from 68°F to 98°F. The expansion coefficient for stainless steel S30100 is 9.4 μin/in°F.

Using the diameter expansion formula:

$d_1 = d_0 (dt \cdot \alpha + 1)$

Substituting the values:

$d_1 = 10.750 \, \text{in} \times \left( (98\,°\text{F} - 68\,°\text{F}) \times 0.0000094 \, \frac{\text{in}}{\text{in}·°\text{F}} + 1 \right) = 10.753 \, \text{in}$

Temperature Expansion Calculator

Calculate the final diameter of a thin circular ring after temperature expansion. This calculator works with both metric and imperial units, provided units are consistent throughout.

Input Parameters:

• d₀: Initial diameter (m, mm, in)
• dt: Temperature difference (°C, °F)
• α: Linear thermal expansion coefficient (m/m°C, mm/mm°C, in/in°F)

References

• Original Source