Question

a bridge is made from 20 m long iron rods at temperature 18 degree Celsius the distance between two rods is 0.4 CM up to what temperature will the bridge be in good shape

Answer 1

Answer:

Temperature = 35.4 C

Step by step explanation:

It is given that the length of the rods = 20m = 2000 cm, temperature T = 18 C, and the distance between the two rods is 0.4 cm.

It is required to find the maximum temperature at which the bridge is still in a good shape.

The bridge will be in a good shape until the two rods expand by 0.2 cm each as the temperature increases. Therefore, let the total expansion be 0.4 cm (2*0.2 cm)

The formula of linear expansion is:

$\frac{\Delta l}{l}=\alpha_1 \Delta T$; where $\Delta l$ is the expansion in the length, l is the length of the rod, $\alpha_1$ is the linear expansion coefficient of iron ($11.5*10^{-6}\:^oC^{-1}$)

$\frac { 0.4 } { 2000 } = 11.5 * 10 ^ { - 6 } \left( T - 18 ^ { \circ } C \right)\\ \\T - 18 = \frac { 0.4 } { 2000 * 11.5 * 10 ^ { - 6 } }\\ \\T = 18 + \frac { 0.4 } { 2000 * 11.5 * 10 ^ { - 6 } }\\ \\T = 35.4 ^ { \circ } C$

Answer 2

Temperature = 35.4 C

Step by step explanation:

It is given that the length of the rods = 20m = 2000 cm, temperature T = 18 C, and the distance between the two rods is 0.4 cm.

It is required to find the maximum temperature at which the bridge is still in a good shape.

The bridge will be in a good shape until the two rods expand by 0.2 cm each as the temperature increases. Therefore, let the total expansion be 0.4 cm (2*0.2 cm)

The formula of linear expansion is:

; where  is the expansion in the length,  is the length of the rod,  is the linear expansion coefficient of iron ()

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