Coefficient of Areal Expansion

The coefficient of areal expansion is defined as the fractional increase in area per unit rise in temperature. It is denoted by αA and has the unit of K^-1 or °C^-1.

Given Data

Volume expansion = 0.30%
Temperature rise = 100°C

Solution

The coefficient of volumetric expansion is given by the formula:

β = 3α

where β is the coefficient of volumetric expansion and α is the coefficient of linear expansion.

Since the volume expansion is given by 0.30%, the volumetric expansion can be calculated as:

β = (0.30/100) x 1000 = 0.003

where 1000 is the volume of the block in cm^3.

Using the formula for volumetric expansion, we get:

V2 = V1 (1 + βΔT)

where V1 is the initial volume, V2 is the final volume, ΔT is the temperature rise and β is the coefficient of volumetric expansion.

Substituting the given values, we get:

V2 = V1 (1 + 0.003 x 100)

V2 = V1 (1.3)

Therefore, the volume of the block increases by 30% of its initial volume.

To find the coefficient of areal expansion, we use the formula:

αA = 2α

where αA is the coefficient of areal expansion and α is the coefficient of linear expansion.

Substituting β = 3α, we get:

αA = 2(β/3)

αA = 2(0.003/3)

Therefore, the coefficient of areal expansion is 0.002 K^-1 or °C^-1.

Conclusion

The coefficient of areal expansion of the metal is 0.002 K^-1 or °C^-1.