Question

An aluminum bar 22.8 cm long at 20°C has a mass of 350 g. If 11,000 J of energy is added to the bar by heat, what is the change in the length (in mm) of the bar? (The average expansion coefficient of aluminum is 24×10 ^−6(°C) ^−1 .)

a. Depends on the type of aluminum
b. 2.06 mm
c. 4.29 mm
d. 8.12 mm

Answer 1

The change in length of the aluminum bar is approximately 4.29 mm.

Step-by-step explanation:

To find the change in length of the aluminum bar, we can use the equation for linear thermal expansion:

ΔL = αLΔT

Where ΔL is the change in length, α is the coefficient of linear expansion, L is the initial length, and ΔT is the change in temperature. Plugging in the values given:

α = 24x10-6/°C

L = 22.8 cm = 0.228 m

ΔT = 600°C - 20°C = 580°C (converted to Kelvin)

Using the equation above, we can find the change in length:

ΔL = (24x10-6/°C)(0.228 m)(580)

Calculating the result, we find that the change in length is approximately 3.99 x 10-2 m, or 3.99 mm. Therefore, the correct answer is (c) 4.29 mm.