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

<p>Force&nbsp; = Aya &lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;&nbsp;<span contenteditable="false"> <math> <mrow> <mi>Δ</mi> <mi>T</mi> </mrow> </math> </span></p><p>Force<span contenteditable="false"> <math> <mrow> <mo>=</mo> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mrow> <mo> (</mo> <mrow> <mn>2</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>1</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>×</mo> <mn>4</mn> <mn>0</mn> <mn>0</mn> </mrow> </math> </span> &lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mi>F</mi> <mo>=</mo> <mn>8</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>5</mn> </mrow> </msup> <mi>N</mi> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;&nbsp;</p><p>&nbsp; <span contenteditable="false"> <math> <mrow> <mi>x</mi> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>5</mn> </mrow> </msup> <mo>=</mo> <mn>8</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>5</mn> </mrow> </msup> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;&nbsp;</p><p>x = 8</p>

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