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A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C ? Coefficient of linear expansion of copper = 1.70 x 10-5K-1.

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As a seasoned tutor on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into the question at hand. We're given the initial diameter of the hole in the copper sheet at 27.0 °C, which is 4.24 cm. We're also provided with...
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As a seasoned tutor on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into the question at hand.

We're given the initial diameter of the hole in the copper sheet at 27.0 °C, which is 4.24 cm. We're also provided with the coefficient of linear expansion of copper, which is 1.70×10−5 K−11.70×10−5K−1.

To find the change in diameter of the hole when the temperature rises to 227 °C, we can use the formula for linear expansion:

ΔL=L0⋅α⋅ΔTΔL=L0α⋅ΔT

Where:

  • ΔLΔL is the change in length (or in our case, diameter),
  • L0L0 is the initial length (or diameter),
  • αα is the coefficient of linear expansion, and
  • ΔTΔT is the change in temperature.

Given that the initial diameter (L0L0) is 4.24 cm and the change in temperature (ΔTΔT) is 227°C−27°C=200°C227°C−27°C=200°C, we can calculate the change in diameter (ΔLΔL).

ΔL=4.24 cm×(1.70×10−5 K−1)×200°CΔL=4.24cm×(1.70×10−5K−1)×200°C
ΔL=4.24 cm×1.70×10−5 K−1×200ΔL=4.24cm×1.70×10−5K−1×200
ΔL=0.014408 cmΔL=0.014408cm

Therefore, the change in diameter of the hole when the copper sheet is heated to 227 °C is approximately 0.0144 cm0.0144cm.

If you need further clarification or assistance with any other questions, feel free to ask!

 
 
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