Expansion of a Square Plate

When a square plate is subjected to a change in temperature, it undergoes thermal expansion. In this scenario, the plate is rigidly held along three edges and forced to move along its fourth edge. We need to determine the expansion along the fourth edge when the temperature increases by T degrees Celsius.

Understanding Thermal Expansion
When an object undergoes a change in temperature, its atoms and molecules vibrate with increased energy. This increased energy causes them to move further apart, leading to an expansion of the object. The amount of expansion depends on the material's coefficient of linear expansion (α), which is a measure of how much the material expands per unit change in temperature.

Expansion Along the Fourth Edge
Since the square plate is rigidly held along three edges, it can only expand along its fourth edge. To calculate the expansion along the fourth edge, we need to consider the coefficient of linear expansion of the material and the original dimensions of the plate.

Let's assume the original length of the fourth edge is 'a' and the coefficient of linear expansion is 'α'. The change in length (∆L) along the fourth edge can be calculated using the formula:

∆L = α * L * ∆T

Where:
∆L = Change in length along the fourth edge
α = Coefficient of linear expansion
L = Original length of the fourth edge
∆T = Change in temperature (T degrees Celsius)

Calculating the Expansion
In this scenario, the original dimension of the square plate is 'a x a'. Since it is a square, all sides are equal in length. Therefore, the original length of the fourth edge is 'a'.

Using the formula mentioned above, the expansion along the fourth edge can be calculated as:

∆L = α * a * ∆T

The expansion (∆L) will depend on the coefficient of linear expansion (α) of the material and the change in temperature (∆T).