The temperature of a 1 m long aluminum rod is 20° C. If the temperature is increased to 70° C, what is the
length of the rod? The coefficient of linear expansion for aluminum is 16 * 10^-6 /(degrees)C
Please help I can not get this.
changein length=L*coeff*deltTemp
= 1m*16E-6*50=800E-6m=.0008m
length of rod now is 1.0008 m
To find the change in length of the aluminum rod, we can use the formula for linear expansion:
ΔL = α * L * ΔT
Here, ΔL represents the change in length, α is the coefficient of linear expansion, L is the original length of the rod, and ΔT is the change in temperature.
Given:
Original temperature (T1) = 20°C
Final temperature (T2) = 70°C
Original length (L) = 1 m
Coefficient of linear expansion (α) = 16 * 10^-6 /(°C)
To determine the change in temperature, we can subtract the original temperature from the final temperature:
ΔT = T2 - T1
= 70°C - 20°C
= 50°C
Now, we can substitute the values into the formula for linear expansion:
ΔL = α * L * ΔT
= (16 * 10^-6 /(°C)) * (1 m) * (50°C)
Calculating this expression will give us the change in length of the rod:
ΔL = (16 * 10^-6 /(°C)) * (1 m) * (50°C)
= (16 * 10^-6 /(°C)) * (1 m) * (50)
= 8 * 10^-4 m
Therefore, the change in length of the aluminum rod is 8 * 10^-4 meters. To determine the final length, add the change in length to the original length:
Final Length = Original Length + Change in Length
Final Length = 1 m + 8 * 10^-4 m
The final length of the rod after the temperature increase is 1.0008 meters.