Question

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

Answer #1

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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