A rod, a sheet and a cube of steel are taken whose temperature is increased from 30 degree Celsius to 80 degree Celsius. If length of rod is 10cm, length of each side of sheet is 10 cm and length of each side of cube is also 10cm. Calculate increment in length, area and volume of rod, sheet and cube respectively (co efficient of linear expansion of steel is 1.2*10^-5 degree Celsius

Dear Student,

Please find below the solution to the asked query:

Given that the coefficient of linear expansion is $\alpha =1.2\times {10}^{-5} per{ }^{0}C$.

Change in length is

$$\begin{gathered} ∆l=l\alpha \left(∆\theta \right)=10\times 1.2\times {10}^{-5}\times \left(80-30\right)=1.2\times 5\times {10}^{-3} \\ \Rightarrow ∆l=6\times {10}^{-3} cm \end{gathered}$$

Change in area of square is,

$$\begin{gathered} ∆A=A2\alpha \left(∆\theta \right)={10}^2\times 2\times 1.2\times {10}^{-5}\times \left(80-30\right)=2.4\times 5\times {10}^{-2} \\ \Rightarrow ∆A=0.12 c{m}^2 \end{gathered}$$

Change in volume of the cube is,

$$\begin{gathered} ∆V=V3\alpha \left(∆\theta \right)={10}^3\times 3\times 1.2\times {10}^{-5}\times \left(80-30\right)=3.6\times 5\times {10}^{-1} \\ \Rightarrow ∆V=1.8 c{m}^3 \end{gathered}$$

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