Find the pressure that has to be applied to the ends of a steel wire of length 10 cm, to keep its length constant…

Q: Find the pressure that has to be applied to the ends of a steel wire of length 10 cm, to keep its length constant when its temperature is raised by 100° C is

( Ys = 2 × 1011 N/m2  αwire = 1.1×10-5/K )

Sol: pressure, $ \large \Delta l = l \alpha \Delta T $

$ \large \frac{\Delta l}{l} = \alpha \Delta T $ …(i)

$\large Y = \frac{F/A}{\frac{\Delta l}{l} }$

$\large Y = \frac{P}{\frac{\Delta l}{l} }$

$\large P = Y \times \frac{\Delta l}{l}$

$\large P = Y \alpha \Delta T $

= 2 × 1011 × 1.1×10-5 × 102

=2.2 × 108 Pa