Question

metal rods of length 20cm each are laid end to end to form a bridge at 25°C. What gap will be provided between consecutive rails for the bridge to withstand 75°C?​

Answer 1

In order for the bridge to withstand a temperature of 75°C, the gap between consecutive rails should be equal to the coefficient of thermal expansion multiplied by the difference between the original and final temperatures. In this case, the coefficient of thermal expansion for metal is approximately 12 x 10-6 K-1, so the gap between the rails should be equal to 12 x 10-6 x 55 = 0.66 mm.

Answer 2

1 mm

Step-by-step explanation:

To find the gap between the metal rods that would allow the bridge to withstand a temperature change from 25°C to 75°C, we need to calculate the increase in length of the metal rods due to thermal expansion.

The linear expansivity of most metals is around 10^-5 / K. So, the increase in length of each metal rod can be calculated as:

ΔL = α * L * ΔT

where α is the linear expansivity, L is the initial length of the rod (20 cm), and ΔT is the change in temperature (75°C - 25°C = 50°C).

Converting the units to SI units, the initial length of the rod becomes 0.2 m and the change in temperature becomes 50 K. So, the increase in length of the rod becomes:

ΔL = 10^-5 / K * 0.2 m * 50 K = 0.001 m = 1 mm

So, the gap between the metal rods should be at least 1 mm to allow for the thermal expansion of the metal rods and avoid buckling or breaking of the bridge under the temperature change from 25°C to 75°C.