Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Answer: The coefficients of areal and volumetric expansion are related to the coefficient of linear expansion for a material. Here's how they compare for metals A and B given that the coefficient of linear expansion of metal A (\(\alpha_A\)) is three times that of metal B (\(\alpha_B\)):
### Areal Expansion
The coefficient of areal expansion (\(\beta\)) is related to the coefficient of linear expansion (\(\alpha\)) by the formula:
\[ \beta = 2\alpha \]
Given that:
\[ \alpha_A = 3\alpha_B \]
The areal expansion coefficients for metals A and B are:
\[ \beta_A = 2\alpha_A \]
\[ \beta_B = 2\alpha_B \]
Substituting \(\alpha_A = 3\alpha_B\):
\[ \beta_A = 2 \times 3\alpha_B = 6\alpha_B \]
So, the areal expansion coefficient of metal A (\(\beta_A\)) is:
\[ \beta_A = 6\alpha_B \]
This means that:
\[ \beta_A = 3 \beta_B \]
Thus, the coefficient of areal expansion of metal A is three times that of metal B.
### Volumetric Expansion
The coefficient of volumetric expansion (\(\gamma\)) is related to the coefficient of linear expansion (\(\alpha\)) by the formula:
\[ \gamma = 3\alpha \]
Given that:
\[ \alpha_A = 3\alpha_B \]
The volumetric expansion coefficients for metals A and B are:
\[ \gamma_A = 3\alpha_A \]
\[ \gamma_B = 3\alpha_B \]
Substituting \(\alpha_A = 3\alpha_B\):
\[ \gamma_A = 3 \times 3\alpha_B = 9\alpha_B \]
So, the volumetric expansion coefficient of metal A (\(\gamma_A\)) is:
\[ \gamma_A = 9\alpha_B \]
This means that:
\[ \gamma_A = 3 \gamma_B \]
Thus, the coefficient of volumetric expansion of metal A is three times that of metal B.
### Summary
- The coefficient of areal expansion (\(\beta\)) of metal A is three times that of metal B.
- The coefficient of volumetric expansion (\(\gamma\)) of metal A is three times that of metal B.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
