Question

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 1

Answer:

The length of the bridge during the hottest part of summer is $L_s = 1235.925 m$

Explanation:

From the question we are told that

    The length of the steel bridge is $L = 1234.567m$

     The temperature for this length is $T_1 = 233.15K$

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

     The coefficient of linear expansion is $\alpha = 11.0123*10^{-6} K^{-1}$

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

             $\Delta L = \alpha L \Delta T$

Substituting value

             $\Delta L = 11.0123*10^{-6} * 1234.567 (333-233.15)$

              $\Delta L = 1.3575 \ m$

The length of the bridge in summer is mathematically evaluated as

         $L_s = L + \Delta L$

Substituting values

         $L_s = 1234.567 + 1.3575$

        $L_s = 1235.925 m$