1. A metal rod 54.0 m long at 32°C is heated to 64°C. By how
much does the length of the rod change (in cm) if the coefficient
of linear expansion of the rod is 32 x 10-6 1/°C?
?? cm
2. A metal rod 77.0 m long at 39°C is heated to 76°C. By how
much does the length of the rod change (in cm) if the coefficient
of linear expansion of the rod is 54 x 10-6 1/°C?
?? cm
1.
Change in length due to temperature is given by,
dL = L0*alpha*dT
here, L0 = length = 54.0 m
alpha = Expansion Coefficient of rod = 32*10^-6 1/K
dT = Tf - Ti
given, Ti = initial temperature = 32 C
Tf = 64 C
then, dT = 64 - 32 = 32 C
So, Using given values:
dL = 54.0*(32*10^-6)*32
dL = 0.0553 m = 5.53*10^-2 m = 5.53 cm
2.
Change in length due to temperature is given by,
dL = L0*alpha*dT
here, L0 = length = 77.0 m
alpha = Expansion Coefficient of rod = 54*10^-6 1/K
dT = Tf - Ti
given, Ti = initial temperature = 39 C
Tf = 76 C
then, dT = 76 - 39 = 37 C
So, Using given values:
dL = 77.0*(54*10^-6)*37
dL = 0.154 = 15.4*10^-2 m = 15.4 cm
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