the length of an aluminium bar of length 80cm increases by 1mm on heating.what is the final temperature of the bar if it was initially at temperature 20 degree celsius?(given:coefficient of linear expansion of aluminium=25×10^-6
.001m=.8m*25E-6*(tf-20)
solve for tf
To find the final temperature of the aluminum bar, we can use the coefficient of linear expansion formula:
ΔL = α * L * ΔT
Where:
ΔL = change in length of the bar
α = coefficient of linear expansion
L = initial length of the bar
ΔT = change in temperature
In this case, we know the change in length (ΔL) is given as 1 mm (0.1 cm), the initial length (L) is 80 cm, the coefficient of linear expansion (α) is 25×10^-6, and the initial temperature (T) is 20 degrees Celsius.
We need to solve for the change in temperature (ΔT):
ΔL = α * L * ΔT
0.1 cm = 25×10^-6 * 80 cm * ΔT
0.1 cm = 2×10^-3 cm * ΔT
Divide both sides of the equation by 2×10^-3 cm:
0.1 cm / 2×10^-3 cm = ΔT
50 = ΔT
Therefore, the change in temperature ΔT is 50 degrees Celsius.
To find the final temperature (Tf), we add the change in temperature (ΔT) to the initial temperature (Ti):
Tf = Ti + ΔT
Tf = 20 degrees Celsius + 50 degrees Celsius
Tf = 70 degrees Celsius
Therefore, the final temperature of the aluminum bar when it increases in length by 1 mm is 70 degrees Celsius.