A rectangular shaped metal plate is heated from 0 to 100 degrees Celsius having initial area of 10 sqcm.given coefficient of linear expansion is 18÷100000000

To understand how the area of a rectangular metal plate changes when it is heated, we need to consider the concept of thermal expansion. When materials are heated, they tend to expand. For a metal plate, this expansion can be calculated using the coefficient of linear expansion.

Understanding Thermal Expansion

Thermal expansion refers to the increase in size of a material as it is heated. The coefficient of linear expansion (α) indicates how much a material expands per degree of temperature change. In this case, the coefficient is given as 18 ÷ 100,000,000, which can be simplified to 1.8 × 10^-7 per degree Celsius.

Calculating Area Expansion

For a rectangular plate, the area expansion can be derived from the linear expansion. The formula for the change in area (ΔA) due to temperature change (ΔT) is:

• ΔA = A₀ × 2α × ΔT

Where:

• A₀ = initial area
• α = coefficient of linear expansion
• ΔT = change in temperature

Plugging in the Values

Now, let's substitute the values into the formula:

• A₀ = 10 sq cm
• α = 1.8 × 10^-7 /°C
• ΔT = 100°C - 0°C = 100°C

Now, we can calculate the change in area:

• ΔA = 10 sq cm × 2 × (1.8 × 10^-7) × 100
• ΔA = 10 sq cm × 3.6 × 10^-5
• ΔA = 0.00036 sq cm

Finding the New Area

To find the new area (A), we add the change in area to the initial area:

• A = A₀ + ΔA
• A = 10 sq cm + 0.00036 sq cm
• A ≈ 10.00036 sq cm

Summary of Results

After heating the rectangular metal plate from 0 to 100 degrees Celsius, the new area of the plate will be approximately 10.00036 square centimeters. This demonstrates how even a small coefficient of linear expansion can lead to measurable changes in area when subjected to significant temperature changes.