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 temp 20 degree celsius? coeff. of linear expansion of aluminium=25

You don't have any units for the coefficients so I don't know where you are but the formula to use is

(dL/L)= k*dT
So plug in dL and L in the proper units and the 25 and solve for dT. Knowing it is 20 at the end calculate the initial T.

To determine the final temperature of the bar, we can use the formula for linear expansion:

ΔL = α * L * ΔT

where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L is the original length, and
ΔT is the change in temperature.

First, let's calculate the change in length (ΔL). Given that the length of the bar increases by 1 mm, we convert it to meters by dividing it by 1000:

ΔL = 1 mm / 1000 = 0.001 m

Now, let's substitute the known values into the formula to find the change in temperature (ΔT):

ΔL = α * L * ΔT

0.001 = 25 * 80 * ΔT

Simplifying the equation:

ΔT = 0.001 / (25 * 80)

ΔT = 0.001 / 2000

ΔT = 5 * 10^(-7)

Therefore, the change in temperature (ΔT) is 5 * 10^(-7) degrees Celsius.

To find the final temperature, we need to add the change in temperature to the initial temperature:

Final Temperature = Initial Temperature + ΔT

Final Temperature = 20 + 5 * 10^(-7)

Final Temperature = 20.0000005 degrees Celsius

Hence, the final temperature of the bar, after heating, is approximately 20.0000005 degrees Celsius.