The length of an aluminium bar of lenth 80cm increase by 1mm on heating. What is the final temperature of the bar if it was initially at temperature 20°C? ( given: coefficient of linear expansion of aluminium = 25×10-6/° C)
changeinlength=origLeng(coeff)(Tf-20)
can you solve that?
To find the final temperature of the bar, we need to use the formula for linear expansion:
ΔL = αLΔT
Where:
ΔL is the change in length of the bar
α is the coefficient of linear expansion
L is the initial length of the bar
ΔT is the change in temperature
In this case, we are given:
ΔL = 1 mm = 0.1 cm (since 1 cm = 10 mm)
L = 80 cm
α = 25×10^(-6)/°C
ΔT = ?
Rearranging the formula, we have:
ΔT = ΔL / (αL)
Plugging in the values, we get:
ΔT = 0.1 cm / (25×10^(-6)/°C * 80 cm)
Simplifying further, we get:
ΔT = 0.1 cm / (2 * 10^(-3)/°C)
ΔT = 0.1 cm / (2 * 10^-1/°C)
ΔT = 5 °C
Finally, to find the final temperature, we add the change in temperature to the initial temperature:
Final temperature = 20°C + 5°C = 25°C
Therefore, the final temperature of the bar is 25°C.