Hello,
I wanted to know if I came to the correct answer in the following problem...
Thank You
I used:
I=LK(To-Tf)
LD=L-I
A silver bar 0.125 meter long is subjected to a temperature change from 200 degrees celsius to 100 degrees celsius. What will be the length of the bar after the temperature change?
My answer:
0.00002363 meter
I don't get that.
deltaL=.125*100*19.2E-6
What you have calculated is the CHANGE in length. The question asks for the LENGTH of the bar. I think you asked a similar question yesterday and Dr Russ pointed out to you that the change was calculated correctly but you needed to add the change to the initial length to obtain the length after the change. This is the same case here; remember that the change in length can be either positive or negative. Note that the temperature changed from 200 to 100 degrees C, meaning that it was cooled. Does that mean the silver bar expanded or contracted?
And I didn't get 4 zeros after the decimal, I obtained only 3 zeros after the decimal.
To determine the correct answer, we need to use the formula you provided, which is:
I = L * K * (To - Tf)
Where:
- I is the change in length
- L is the original length of the silver bar
- K is the coefficient of linear expansion of silver
- To is the initial temperature
- Tf is the final temperature
In this case, the change in length (I) is what we want to find.
Given:
- L = 0.125 meter (original length of the silver bar)
- K is not provided, but we can assume it to be the coefficient of linear expansion of silver, which is approximately 0.000023 (1/°C).
- To = 200 degrees Celsius (initial temperature)
- Tf = 100 degrees Celsius (final temperature)
To calculate I:
I = 0.125 * 0.000023 * (200 - 100) = 0.000575 meter
Therefore, the change in length (I) of the silver bar is 0.000575 meter.
Now we can find the length of the bar after the temperature change by subtracting the change in length (I) from the original length (L):
Length after temperature change = L - I = 0.125 - 0.000575 = 0.124425 meter
So, the correct answer should be approximately 0.124425 meter, rather than 0.00002363 meter.