Question

The inner diameter of a copper ring is 0.500 cm at 273 K. To what temperature, in kelvin, should the ring be heated up such that its diameter becomes 0.501 cm? αCu = 17 x 10^-6 K.

Answer 1

Solution-

Given data:-

Initial inner diameter= d₁=0.500 cm

Final inner diameter=d₂= 0.501 cm

Initial temperature= T₁=273 K

_Cu= 17×10^-6 /K= coefficient of linear expansion

As metal is heated it expands. So coefficient of linear expansion is given as,

L= L T

L= initial length of ring= Circumference of ring

So, L= 2r= d

So, L= d

So,

d= d T

d= d T

So,

d₂-d₁₌ d₁ (T₂-T₁)

So, put the values,

0.501-0.500=17×10^-6*0.500*(T₂-273)

0.001=8.5*10^-6*(T₂-273)

0.001/8.5*10^-6 =T₂-273

0.000117*10^6=T₂-273

117=T₂-273

T₂=117+273

T₂=390 K

So ring should be heated at 390 K.