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

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

Step-by-step 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 = (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`