A steel rod of length 4 m is welded to the end of an aluminum rod of length 3 m (lengths measured at 23 °C). The combination rod is then heated to 198 °C. What is the length of the combination rod at 198 °C? (The linear expansion coefficients for steel and aluminum are 1.3 10-5 °C−1 and 2.2 10-5 °C−1, respectively. Enter your answer to three significant figures.)

Question

A steel rod of length 4 m is welded to the end of an aluminum rod of length 3 m (lengths measured at 23 °C). The combination rod is then heated to 198 °C. What is the length of the combination rod at 198 °C? (The linear expansion coefficients for steel and aluminum are 1.3 10-5 °C−1 and 2.2 10-5 °C−1, respectively. Enter your answer to three significant figures.)

I know the equation to be used is, delta length=(linear coefficient of expansion)(length)(delta temperature)

i am confused as to what to use for length on the right side of the equation, and what to subtract from delta length

Answer 1

Hmmm. Do it in two parts, steel expansion, and aluminum expansion, then add the two expansions.

Answer 2

What do i use for delta length?

Answer 3

That is what you are solving for.

deltaLengthAl= coeff*changetemp*lengthorigAl
deltaLengFe= coeff*changetemp*lenghorigFe

Total changelenght= sum of above

Answer 4

it didn't give me the correct answer

Answer 5

To find the length of the combination rod at 198 °C, we can use the equation for linear expansion:

delta length = (linear coefficient of expansion) * (length) * (delta temperature)

In this case, we have two materials with different linear coefficients of expansion, so we need to consider them separately.

Let's start with the steel rod. We can calculate the change in length for the steel rod using the equation:

delta length_steel = (linear coefficient of expansion_steel) * (length_steel) * (delta temperature)

delta length_steel = (1.3 * 10^(-5) °C^(-1)) * (4 m) * (198 °C - 23 °C)

Next, we can calculate the change in length for the aluminum rod using the equation:

delta length_aluminum = (linear coefficient of expansion_aluminum) * (length_aluminum) * (delta temperature)

delta length_aluminum = (2.2 * 10^(-5) °C^(-1)) * (3 m) * (198 °C - 23 °C)

Now, let's calculate the final length of the combination rod. We need to add the change in length of the steel rod to the original length of the steel rod, and do the same for the aluminum rod:

length_combination = length_steel + delta length_steel + length_aluminum + delta length_aluminum

Remember to use the lengths at 23 °C.

Finally, substitute the values and calculate the length of the combination rod at 198 °C. Round your answer to three significant figures.