A steel rod is 2.55 cm long at 16 o C in an operating room. It is placed in a patient's leg where it rises to 37 o C. What will the change in length be?
coefficient of linear expansion for steel 13.0 x10^-6
I am getting .0006915 but the answer is .000643 according to book
What am I doing wrong or does the book have a misprint?
13.0x10^-6 x 2.55 cm x (37-16) =.0006915
your work looks correct
medical alloys may have varying expansion coefficients
... where did the 1.30E-7 come from?
my book says that is what the expansion coefficient is for steel
To calculate the change in length correctly, you need to convert the length of the rod from cm to meters. The coefficient of linear expansion is given per meter, so the length should also be in meters.
1 cm is equal to 0.01 meters, so the length of the rod in meters is:
2.55 cm * 0.01 = 0.0255 meters
Now you can proceed with the calculation:
Change in length = (coefficient of linear expansion) * (original length) * (change in temperature)
Change in length = (13.0 x 10^-6) * (0.0255) * (37 - 16)
Change in length = 0.0003405 * 21
Change in length = 0.0071475 meters
Now, to convert the result back to cm:
Change in length = 0.0071475 meters * 100 = 0.71475 cm
So, the correct answer is approximately 0.71475 cm, which is different from what you calculated. It seems like the book answer of 0.000643 cm is incorrect, as it doesn't seem to match the given values and calculations.
To solve this problem, you need to use the coefficient of linear expansion for steel and the given temperatures. Let's break down the steps to identify the discrepancy between your answer and the answer given in the book.
The formula for finding the change in length due to temperature change is:
ΔL = α * L * ΔT,
Where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L is the original length, and
ΔT is the change in temperature.
Using the given data:
α = 13.0 x 10^-6 (coefficient of linear expansion for steel)
L = 2.55 cm (original length)
ΔT = 37 - 16 = 21 (change in temperature)
Plugging in the values, we get:
ΔL = (13.0 x 10^-6) * (2.55 cm) * (21)
ΔL = 0.0007095 cm, or 7.095 x 10^-4 cm
Therefore, the change in length should be approximately 0.0007095 cm, not 0.0006915 cm as you calculated.
It seems that there might be a calculation error in your calculation. Please recheck your calculation to ensure that you are using the correct values and performing the calculations accurately. If you still get a different answer, you may want to consult the book and verify if there is indeed a misprint.