Temperature to Length Calculator

Original Length (L_0):

Coefficient of Thermal Expansion (α):

Initial Temperature:

Final Temperature:

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1. What is the Thermal Expansion Calculator?

Definition: The Thermal Expansion Calculator determines the change in length and total length of a material due to a temperature change using the formula \(\Delta L = L_0 \cdot \alpha \cdot \Delta T\).

Purpose: Helps engineers predict dimensional changes in materials under thermal loads.

Reference:Applied Strength of Materials for Engineering Technology

http://www.etcs.pfw.edu/~dupenb/ET_200/Applied%20Str%20of%20Mat%20for%20ET%20v14%20July%202018.pdf

2. How Does the Calculator Work?

Formula:

\(\Delta L = L_0 \cdot \alpha \cdot \Delta T\), \(L_{\text{total}} = L_0 + \Delta L\)

Where:

\(\Delta L\): Change in length
\(L_0\): Original length
\(\alpha\): Coefficient of thermal expansion
\(\Delta T\): Temperature change
\(L_{\text{total}}\): Total length after expansion

Steps:

Step 1: Input Original Length. Enter the initial length (e.g., 100 mm).
Step 2: Select or Input Coefficient of Thermal Expansion. Choose a material (e.g., Steel: 0.000012 /°C) or enter a custom value.
Step 3: Input Temperatures. Enter initial and final temperatures (e.g., 20°C and 100°C).
Step 4: Calculate. The calculator computes the change in length and total length.

3. Importance of Thermal Expansion Calculation

Calculating thermal expansion is crucial for:

Material Design: Ensures components fit under temperature variations.
Structural Integrity: Prevents stress from expansion or contraction.
Unit Consistency: Supports conversions across metric and imperial units.

4. Using the Calculator

Example: Length = 100 cm, Material = Aluminum (0.000023 /°C), Initial Temp = 20°C, Final Temp = 100°C:

Step 1: \(\Delta T = 100 - 20 = 80 \, \text{°C}\).
Step 2: \(\Delta L = 100 \cdot 0.000023 \cdot 80 = 0.184 \, \text{cm}\).
Step 3: \(L_{\text{total}} = 100 + 0.184 = 100.184 \, \text{cm}\).

5. Frequently Asked Questions (FAQ)

Q: What is the coefficient of thermal expansion?
A: It’s the fractional change in length per degree of temperature change.

Q: Can I use Fahrenheit?
A: Yes, the calculator converts °F to °C internally.

Q: Is this accurate for all materials?
A: Yes, if \(\alpha\) is correctly input or selected for the material.