A steel rod with y = 2.0 $\times$ 10¹¹ Nm^$-$2 and $\alpha$ = 10^$-$5 $^\circ$C^$-$1 of length 4 m and area of cross-section 10 cm² is heated from 0$^\circ$C to 400$^\circ$C without being allowed to extend. The tension produced in the rod is x $\times$ 10⁵ N where the value of x is ____________.

Given, the Young's modulus of the steel rod, Y = 2 $\times$ 10¹¹ Pa<br/><br/>Thermal coefficient of the steel rod, $\alpha$ = 10^$-$5$^\circ$C<br/><br/>The length of the steel rod, l = 4 m<br/><br/>The area of the cross-section, A = 10 cm²<br/><br/>The temperature difference, $\Delta$T = 400$^\circ$C<br/><br/>As we know that,<br/><br/>Thermal strain = $\alpha$ $\Delta$T<br/><br/>Using the Hooke's law<br/><br/>Young's modulus (Y) = $${{Thermal\,stress} \over {Thermal\,strain}} = {{F/A} \over {\alpha \,\Delta \,T}}$$<br/><br/>Thermal stress, $F = YA\,\alpha \,\Delta \,T$<br/><br/>Substitute the values in the above equation, we get<br/><br/>$$F = 2 \times {10^{11}} \times 10 \times {10^{ - 4}} \times {10^{ - 5}} \times (400)$$<br/><br/>$= 8 \times {10^5}N$<br/><br/>Comparing with, $F = x \times {10^5}N$<br/><br/>The value of the x = 8.