Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
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.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
