How to compute specific surface energy for cubes of varying sizes?

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  • #1
Guilty_Way6122
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Homework Statement
Compute the specific surface energy in J/g for a 1-gram cube of table salt with an edge of 0.77 cm, when it is split into
(a) 1 µm side cubes
(b) 1 nm side cubes
(c) 1nm radius sphere
Relevant Equations
NaCl: Surface energy, γ = 0.2 J/m^2 ; Edge energy, E = 3 x 10^-11 J/m
I got these values but I wanted to make sure I was doing it the correct way
a) 0.548 J/g for system of 1 µm cubes
b) 9.131 x 10^19 J/g for system of 1 nm cubes
c) 273.890 J/g for system of 1 nm radius spheres
 
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  • #2
As you haven't shown us the way you're doing it, how can we tell if you're doing it the right way?
But compare the magnitudes of your numbers. Do you really expect 1 nm cubes and 1 nm spheres to be so different? Looks like something's wrong somewhere. Please show your working.
 
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FAQ: How to compute specific surface energy for cubes of varying sizes?

What is specific surface energy and why is it important for cubes of varying sizes?

Specific surface energy, also known as surface free energy, is the energy required to create a unit area of a surface. It is important for cubes of varying sizes because it affects properties such as adhesion, wetting, and surface reactions. Understanding specific surface energy helps in predicting and controlling these properties in materials science and engineering applications.

How do you calculate the surface area of a cube?

The surface area of a cube can be calculated using the formula \( A = 6a^2 \), where \( a \) is the length of one side of the cube. This formula accounts for the six faces of the cube, each with an area of \( a^2 \).

What is the formula to compute specific surface energy for a cube?

The specific surface energy \( \gamma \) can be computed using the formula \( \gamma = \frac{E_{\text{surface}}}{A} \), where \( E_{\text{surface}} \) is the total surface energy and \( A \) is the total surface area of the cube. For a cube, this becomes \( \gamma = \frac{E_{\text{surface}}}{6a^2} \).

How does the size of the cube affect its specific surface energy?

The size of the cube affects its specific surface energy in that smaller cubes have a higher surface-to-volume ratio, potentially leading to higher specific surface energy. This is because a greater proportion of the atoms or molecules are at or near the surface, which can increase the total surface energy relative to the cube's size.

What are the practical steps to measure specific surface energy experimentally?

To measure specific surface energy experimentally, you typically need to: (1) prepare a clean, well-defined surface of the material, (2) use techniques such as contact angle measurements, atomic force microscopy (AFM), or surface tension measurements to gather data, and (3) apply theoretical models or empirical correlations to interpret the data and calculate the specific surface energy.

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