Question

A metal rod 80cm long lengthens by 0.090cm when its temperature rises by 93.6$^o$C. What is the linear expansivity of the metal

(a)0.0012/k
(b)0.000012/k
(c)12/k
(d)1.2/k

Answer 1

Answer: (b)0.000012/k

Step-by-step explanation:

The linear expansion of the metal rod is given by

`\Delta L= L_0 \alpha \Delta T`

where

`\Delta L=0.090 cm` is the linear expansion

`L_0 = 80 cm` is the initial length of the rod

`\alpha` is the linear expansivity

`\Delta T=93.6^(\circ)C=93.6 K` is the increase in temperature

By re-arranging the equation, we find the linear expansivity:

`\alpha = (\Delta L)/(L_0 \Delta T)=(0.090 cm)/((80 cm)(93.6K))=0.000012 K^(-1)`