00:01
For this problem, we are told that a thin silver wire has length l equals 18 centimeters when the temperature is 30 degrees celsius.
00:08
We are asked to estimate delta l when t decreases to 25 degrees celsius if the coefficient of thermal expansion is k equals 1 .9 times 10 to negative 5 degrees celsius inverse.
00:22
So to begin, we have that dl by dt equals kl, and we can then say that, dl is going to equal dl by dt, that should be a capital t temperature, dl by dt times dt.
00:40
So what we need to do is figure out the derivative with respect to temperature and multiply it by the change in temperature.
00:48
So we have then that dl by dt, you need to figure out here, dl by dt when t equals 30 is going to equal 1 .9 times 10 to the negative 5 times the length, which is 18.
01:10
So we have that's degree celsius inverse, and then we multiply by 18 centimeters...