A steel rod of length 1 m is welded to the end of an aluminum rod of length 2 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.)

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To find the final length of the combination rod at 198 °C, we need to take into account the thermal expansion of both the steel and aluminum rods.

The formula to calculate the thermal expansion is given by:

ΔL = α * L * ΔT

Where:
ΔL is the change in length
α is the linear expansion coefficient
L is the original length
ΔT is the change in temperature

Let's calculate the change in length for the steel rod first:
ΔL_steel = α_steel * L_steel * ΔT

Substituting the given values:
α_steel = 1.3 * 10^-5 °C^-1
L_steel = 1 m
ΔT = 198 °C - 23 °C = 175 °C

ΔL_steel = 1.3 * 10^-5 °C^-1 * 1 m * 175 °C

Next, let's calculate the change in length for the aluminum rod:
ΔL_aluminum = α_aluminum * L_aluminum * ΔT

Substituting the given values:
α_aluminum = 2.2 * 10^-5 °C^-1
L_aluminum = 2 m
ΔT = 198 °C - 23 °C = 175 °C

ΔL_aluminum = 2.2 * 10^-5 °C^-1 * 2 m * 175 °C

Now, we can find the total change in length by adding the change in length of both rods:
ΔL_combination = ΔL_steel + ΔL_aluminum

Finally, we can find the final length of the combination rod by adding the initial length of the aluminum rod to the total change in length:
Length_combination = L_aluminum + ΔL_combination

Substituting the calculated values:
Length_combination = 2 m + (ΔL_steel + ΔL_aluminum)

Once you calculate ΔL_steel and ΔL_aluminum, substitute them into the equation above, and perform the calculations, you will find the final length of the combination rod at 198 °C.

Please note that the final answer should be rounded to three significant figures.