Question

At 1000 K, the linear thermal expansion coefficients of graphite, parallel and perpendicular to the graphite layers, are \( 0.8 \times 10^{-6} \, \text{K}^{-1} \) and \( 29 \times 10^{-6} \, \text{K}^{-1} \), respectively. The percentage increase in the volume of graphite when heated from 900 K to 1100 K is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).

Hint:

For materials with different expansion coefficients, use the average expansion coefficient for volumetric expansion.

Answer 1

Correct Answer: 0.6

The volumetric expansion \( \Delta V \) for a material is calculated using the formula:
\[ \Delta V = \beta \Delta T \] Where:
- \( \beta \) is the volumetric coefficient of expansion, and
- \( \Delta T = 1100 - 900 = 200 \, \text{K} \).
The coefficient of volumetric expansion for graphite, \( \beta \), is calculated as the sum of the linear expansions in all directions. Since graphite expands differently along the directions parallel and perpendicular to the layers, we calculate the average expansion coefficient for the entire material. The average coefficient \( \beta \) is given by:
\[ \beta = 3 \times (0.8 \times 10^{-6} \, \text{K}^{-1}) + (29 \times 10^{-6} \, \text{K}^{-1}) = 0.60 \, % \] Thus, the percentage increase in volume is approximately \( 0.60 \, % \).