The length of an aluminium bar of length 80 cm increases by 1 mm on heating.What is the final temperature of the bar if it was initially at temperature 20 degree Celsius? (coefficient of linear expansion of aluminium =25*10-6/degree Celsius)
change in L/L = 25*10^-6 (T-20)
.1/80 = 1/800 = 25* 10^-6 (T-20)
T-20 = 10^6/2*10^4 =50
T = 70 deg C
To find the final temperature of the aluminum bar, we can use the concept of linear expansion and apply the formula:
ΔL = α * L0 * ΔT
where:
ΔL is the change in length of the bar
α is the coefficient of linear expansion
L0 is the initial length of the bar
ΔT is the change in temperature of the bar
Given:
ΔL = 1 mm = 0.1 cm (since 1 cm = 10 mm)
L0 = 80 cm
α = 25 * 10^(-6) / degree Celsius (coefficient of linear expansion of aluminum)
Let's substitute these values into the formula and solve for ΔT:
0.1 cm = (25 * 10^(-6) / degree Celsius) * 80 cm * ΔT
Simplifying the equation, we have:
0.1 cm = 2 * 10^(-4) * ΔT
Dividing both sides by 2 * 10^(-4), we get:
ΔT = 0.1 cm / (2 * 10^(-4))
ΔT = 500 degree Celsius
Now, to find the final temperature (Tf), we need to add the change in temperature (ΔT) to the initial temperature (Ti):
Tf = Ti + ΔT
Tf = 20 degree Celsius + 500 degree Celsius
Tf = 520 degree Celsius
Therefore, the final temperature of the aluminum bar, after an increase in length of 1 mm, is 520 degree Celsius.