A steel bridge is 1000m long at -20 degreesC in winter. What is the change in length when the temperature rises to 40 degreesC in summer?
The average coefficient of linear expansion of steel is 11x10^-6/C degrees
The answer is D.
This can be easily determined by using the formula for linear expansion due to temperature (or linear thermal expansion). This formula is stated as
change in length = alpha times the original length of the substance times the change in temperature. In this case, alpha is the average coefficient of linear expansion.
In the example you provide, you have given us all the information on the right side of the equation so all you have to do is multiply. When you mulitply the three numbers (1000 meters, the coefficient, and 60, which is the change in temperature) you get
Change in length of bridge is given by the formula:
L2 - L1 = L1*(t2 - t1)*E
L1 = Initial length of bridge = 1000 m (Given)
L2 = Final length of bridge
t1 = temperature in winter = -20 degrees C (Given)
t2 = temperature in summer = 40 degrees C (Given)
E = Coefficient of linear expansion = 11*(10^-6)/C degrees
Substituting these values in the above equation we get:
L2 - L1 = 1000*[40 - (-20)]*11*(10^-6) = 66*(10^-2) = 0.66 m
Therefore change in length is 0.66 m.
Thus option D0 is correct.
The required relation to find the length of the steel bridge after a raise in tempearature is given by:
L2 = L1 (1+alpha*(t2-t1)), where L1 is its initial length of the bridge at temperature t1 and L2 is the length of the bridge at temperature t2 and alpha is the coefficient of the linear expansion of the material of the bridge. Substituting the given values and solving for L2 -L1 we get:
L2-L1 = L1*alpha*(t2-T1),. S ubstituting the values,