If $2.2 \times 10^{x} a t m$ pressure has to be applied to the ends of a steel cylinder to keep its length constant on raising its temperature by $100^{\circ}$ , find the value of $x$ .

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Solution

Variation of length with temperature is given by
$l_{t} = l_{0} (1 + α Δ t)$ or $\frac{Δ l}{l_{0}} = α Δ t = ε$ (1)
But $ε = \frac{σ}{E}$ ,
Thus $σ = α Δ t E$ , which is the sought stress of pressure.
Putting the value of $α$ and $E$ from Appendix and taking $Δ t = 100^{\circ}$ , we get
$σ = 2.2 \times 10^{3} a t m$

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