Question

if the area of an automobile windshield is 60.0cm by 150 cm on a 20°C day, what is the change in area when the temperature changed from 0°C to 36°C.

The coefficient of linear expansion of glass is 9 ´ 10-6/°C

Answer 1

Due to temperature increase, expansion in length of windshield will be given by:

dL = L0*alpha*dT

L0 = initial length = 150 cm = 1.5 m

alpha = coefficient of linear expansion of glass = 9*10^-6 /C

dT = 36 - 0 = 36 C

So,

dL = L1 - L0 = L0*alpha*dT

L1 = L0 + L0*alpha*dT

L1 = 1.5 + 1.5*9*10^-6*36

L1 = 1.500486 m = 150.0486 cm

Similarly, new width of windshield will be

w1 = w0 + w0*alpha*dT

w0 = initial width = 60 cm = 0.6 m

w1 = 0.6 + 0.6*9*10^-6*36

w1 = 0.6001944 m = 60.01944 cm

Now

Initial Area = A0 = L0*w0 = 60*150 = 9000 cm^2

A1 = New Area = L1*w1 = 150.0486*60.01944 = 9005.83294 cm^2

dA = A1 - A0 = 9005.83294 - 9000

dA = Change in Area = 5.83294 cm^2

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answered by: anonymous