A rectangular plate of glass initially has the dimensions 0.200 m by 0.300 m . The coefficient of linear expansion for the glass is `9.00xx10^(-6)//K` . What is the change in the plate's area if it's temperature is increased by 20.0 K ?

Answer

To find the change in area of the rectangular glass plate when its temperature is increased, we can follow these steps:

### Step 1: Calculate the Initial Area
The initial area \( A_0 \) of the rectangular plate can be calculated using the formula:
\[ A_0 = \text{length} \times \text{breadth} \]
Given dimensions are:
- Length = 0.200 m
- Breadth = 0.300 m

So,
\[ A_0 = 0.200 \, \text{m} \times 0.300 \, \text{m} = 0.0600 \, \text{m}^2 \]

### Step 2: Identify the Coefficient of Linear Expansion and Temperature Change
The coefficient of linear expansion \( \alpha \) for glass is given as:
\[ \alpha = 9.00 \times 10^{-6} \, \text{K}^{-1} \]
The change in temperature \( \Delta T \) is:
\[ \Delta T = 20.0 \, \text{K} \]

### Step 3: Calculate the Change in Area
The change in area \( \Delta A \) due to temperature change can be calculated using the formula:
\[ \Delta A = A_0 \cdot 2\alpha \Delta T \]
Substituting the values we have:
\[ \Delta A = 0.0600 \, \text{m}^2 \cdot 2 \cdot (9.00 \times 10^{-6} \, \text{K}^{-1}) \cdot (20.0 \, \text{K}) \]

Calculating this step-by-step:
1. Calculate \( 2 \alpha \Delta T \):
\[ 2 \cdot (9.00 \times 10^{-6}) \cdot (20.0) = 3.60 \times 10^{-4} \]
2. Now calculate \( \Delta A \):
\[ \Delta A = 0.0600 \cdot 3.60 \times 10^{-4} = 2.16 \times 10^{-5} \, \text{m}^2 \]

### Final Result
The change in the area of the glass plate is:
\[ \Delta A = 2.16 \times 10^{-5} \, \text{m}^2 \]

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