What is the relationship between area and volume expansivity ?
That is what is the formula connecting area and volume expansivity?
ä = Liner expansivity
B = area expansivity
¥ = cubic expansivity
Since we know that
Area expansivity ( B ) = 2 Linear expansivity ( ä )
Cubic expansivity ( ¥ ) = 3 linear expansivity ( ä )
I.e
B = 2ä ======> ( i )
¥ = 3ä ======> ( ii )
Interchanging
ä = B/2 ======> ( iii )
ä = ¥/3 =======> ( iv )
Equating eqn ( iii ) and ( iv )
B/2 = ¥/3
Cross multiply
3B = 2¥
B = ⅔¥
Hence proved...
Q.E.D🔥🔥🔥
the relashonship is bitter is equal to 2 alpha
gama is equal to 3 alpha
Can I ask a question.....wat is d equation that connects linear, area and volume expansivity...... I need answers urgently✨🖤
L=S=0
The relationship between area expansivity and volume expansivity is based on the concept of thermal expansion, which refers to the change in size or dimensions of a substance due to changes in temperature.
Area expansivity (β) measures how the area of an object changes with respect to a change in temperature, while volume expansivity (γ) measures how the volume of an object changes with respect to a change in temperature.
The connection between area expansivity and volume expansivity can be derived by considering the relationship between area and volume. In a three-dimensional object, the volume (V) is related to the area (A) through the third dimension, which we will call h (height).
We can express the volume as V = A * h, where A is the area of a face perpendicular to the height h.
Now, if we consider the change in volume (∆V) and the change in area (∆A) due to a change in temperature (∆T), we can write:
∆V = (∆A * h)
It's important to note that the height (h) remains constant when we are considering changes in area and volume due to temperature variations.
The coefficients of linear expansion (α) and volume expansion (β) are defined as:
α = (∆L / L * ∆T), where ∆L is the change in length, L is the initial length, and ∆T is the change in temperature.
β = (∆V / V * ∆T), where ∆V is the change in volume, V is the initial volume, and ∆T is the change in temperature.
To establish a relationship between area expansivity and volume expansivity, we can substitute the equation for ∆V above:
∆V = (∆A * h)
Then, rearranging the equation:
∆V = (∆A * ∆L)
Dividing both sides of the equation by V, we get:
(∆V / V) = (∆A * ∆L) / V
Now, recalling that (∆L / L) is the linear expansivity (α), we can rewrite the equation as:
β = (∆A / A * ∆V / V)
Replacing (∆A / A) with the area expansivity (β) and (∆V / V) with the volume expansivity (γ), we finally get:
β = γ
Thus, the formula connecting area expansivity (β) and volume expansivity (γ) is simply β = γ.
its raised the power of the [e. 3 square to 3 cube] is 9 to 27
which is gotten from their expansivity