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In deserts the temperatures can reach extreme values in deep of summer and winter. A steel bridge is being constructed and it is supposed to be 1234.567 m long at 233.15 K in the coldest possible winter. What will be the possible length of this bridge when the temperature rises to a possible extreme of +140.0°F in hottest part of summer? The average coefficient of linear expansion of the steel is 11.0123 × 10-6 K-1.

Answer :

okpalawalter8

Answer:

The length of the bridge during the hottest part of summer is [tex]L_s = 1235.925 m[/tex]

Explanation:

From the question we are told that

    The length of the steel bridge is [tex]L = 1234.567m[/tex]

     The temperature for this length is [tex]T_1 = 233.15K[/tex]

     The temperature at summer [tex]T_2 = + 140.0F = \frac{140 - 32}{180} *100 + 273= 333 K[/tex]

     The coefficient of linear expansion is [tex]\alpha = 11.0123*10^{-6} K^{-1}[/tex]

Generally the change in length of the steel bridge is mathematically represented as

             [tex]\Delta L = \alpha L \Delta T[/tex]

Substituting value

             [tex]\Delta L = 11.0123*10^{-6} * 1234.567 (333-233.15)[/tex]

              [tex]\Delta L = 1.3575 \ m[/tex]

The length of the bridge in summer is mathematically evaluated as

         [tex]L_s = L + \Delta L[/tex]

Substituting values

         [tex]L_s = 1234.567 + 1.3575[/tex]

        [tex]L_s = 1235.925 m[/tex]

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