An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of15 degrees cel. Both rods have the same diameter. The rods are joined end-to-end to form a rod 90.0 cm long. The coefficients of linear expansion of aluminum and steel are2.4x10^-5k^-1 and1.2x10^-5k^-1 respectively. The temperature is raised to90degrees cel. The increase in the length of the joined rod, in mm,

To find the increase in the length of the joined rod, we need to calculate the change in length for each material and then add them together.

The change in length of a material can be calculated using the formula:

ΔL = α * L * ΔT

Where:
ΔL = Change in length
α = Coefficient of linear expansion
L = Original length
ΔT = Change in temperature

For the aluminum rod:
α_aluminum = 2.4x10^-5 K^-1
L_aluminum = 10.0 cm = 0.1 m
ΔT = 90 °C - 15 °C = 75 °C

ΔL_aluminum = (2.4x10^-5 K^-1) * (0.1 m) * (75 °C)
= 18x10^-5 K * m

For the steel rod:
α_steel = 1.2x10^-5 K^-1
L_steel = 80.0 cm = 0.8 m
ΔT = 90 °C - 15 °C = 75 °C

ΔL_steel = (1.2x10^-5 K^-1) * (0.8 m) * (75 °C)
= 7.2x10^-5 K * m

Now, we can find the total change in length of the joined rod by adding the changes in length of aluminum and steel:

ΔL_total = ΔL_aluminum + ΔL_steel
= 18x10^-5 K * m + 7.2x10^-5 K * m
= 25.2x10^-5 K * m

Finally, we convert the change in length to millimeters:

ΔL_total_mm = ΔL_total * 1000 mm/m
= 25.2x10^-5 K * m * 1000 mm/m
= 25.2x10^-2 mm
= 0.252 mm

Therefore, the increase in the length of the joined rod when the temperature is raised to 90 °C is 0.252 mm.