Question

 

14. A dime has a diameter of 1.8000 cm at 20C. The dime is made of mostly zinc, for which the 

coefficient of linear expansion is 2.6 10 −5C−1.  

 

(a) What would its diameter be on a hot day at 48.0C?  

(b) What is its diameter on a cold night at −53.0C? 

Answer 1

Solution.

$D_0=1.8000cm;$

$T_0=20^oC;$

$\alpha=2.61\sdot10^{-5}C^{-1};$

$a)T=48.0^oC;$

$\Delta D=\alpha D_0\Delta T;$

$\Delta D=2.61\sdot10^{-5}\sdot1.8000\sdot(48.0-20)=0.0013cm;$

$D=D_0+\Delta D;$

$D=1.8000+0.0013=1.8013cm;$

$b) T=-53.0^oC;$

$\Delta D=\alpha D_0\Delta T;$

$\Delta D=2.61\sdot10^{-5}\sdot1.8000\sdot(-53.0-20)=-0.0034cm;$

$D=D_0+\Delta D;$

$D=1.8000-0.0034=1.7966cm;$

Answer: $a)D=1.8013cm;$

$b)D=1.7966cm.$