Question

A certain ceramic has a theoretical density and sintered density of \( 6.76 \, \text{g/cm}^3 \) and \( 6.60 \, \text{g/cm}^3 \), respectively. The green compact has 18 volume percent porosity. For a sintered cube of side 2 cm, the required side of the cubic green compact in cm is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).

Hint:

When calculating the required side length for sintered materials, account for porosity and use the relation between theoretical and sintered densities.

Answer 1

Correct Answer: 2.1

The theoretical density of the green compact is related to the sintered density by the following equation:
\[ \text{Sintered Density} = \text{Theoretical Density} \times (1 - \text{Porosity}) \] Given:
- Theoretical density = \( 6.76 \, \text{g/cm}^3 \),
- Sintered density = \( 6.60 \, \text{g/cm}^3 \),
- Porosity = \( 18 \, % \).
Substituting the values:
\[ \text{Porosity} = 1 - \frac{\text{Sintered density}}{\text{Theoretical density}} = 1 - \frac{6.60}{6.76} = 0.0236 \] Now, using the formula to find the required side length of the cubic green compact:
\[ \text{Side of cubic green compact} = \left( \frac{\text{Sintered Volume}}{(1 - \text{Porosity})} \right)^{1/3} \approx 2.11 \, \text{cm}. \] Thus, the required side of the cubic green compact is approximately \( 2.11 \, \text{cm} \).