Question

If $2.2\times {10}^{x}atm$ 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 $x$.

Answer 1

Variation of length with temperature is given by
$l_t=l_0(1+\alpha \Delta t)$ or $\frac{\Delta l}{l_0}=\alpha \Delta t=\epsilon$ (1)
But $\epsilon =\frac{\sigma }{E}$,
Thus $\sigma =\alpha \Delta tE$, which is the sought stress of pressure.
Putting the value of $\alpha$ and $E$ from Appendix and taking $\Delta t={100}^{\circ }$, we get
$\sigma =2.2\times {10}^{3}atm$