A bridge is made from 20 m long iron rods- At temperature 18-C- the distance between two rods is 0-4 cm- Up to what temperature will the bridge be in good shape-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Thermal Expansion

A bridge is m...

Question

A bridge is made from $20$ m long iron rods. At temperature $18^{\circ} C$ , the distance between two rods is $0.4$ cm. Up to what temperature will the bridge be in good shape?

Open in App

Solution

Length of the iron rod $= 20 m = 2000 c m$ at $18^{\circ} C$
Distance between the length of two rods, $= 0.4 c m$ Temperature coefficient of linear expansion of iron $= 11.5 \times 10^{- 6} C^{- 1}$
The bridge will be in good shape until both the rods expand by $0.2$ cm as the temperature is increased. Let at temperature T, both the rods expand by $0.2$ cm i.e. the total expansion is $0.4$ cm.
Using the formula for the linear expansion of solids, we have
$\frac{Δ l}{l} = a_{l} Δ T$
$∴ \frac{0.4}{2000} = 11.5 \times 10^{- 6} \times (T - 18)$
$T = 18 + \frac{0.4}{2000 \times 11.5 \times 10^{- 6}} = {35.4}^{\circ} C$

Suggest Corrections

Similar questions

A bridge is made from $20 m$ long iron rods. At temperature $18^{\circ} C$ , the distance between two rods is $0.4 c m$ . Up to what temperature will the bridge be in good shape?

(Take coefficient of Linear expansion of iron is $11.5 \times 10^{- 6}^{\circ} C$ )

Q. Solve the following examples.

a.What must be the temperature in Fahrenheit so that it will be twice its value in Celsius?

b. A bridge is made from 20 m long iron rods. At temperature 18^∘C, the distance between two rods in 0.4 cm. Up to what temperature will the bridge be in good shape?

c. At 15^∘C the height of Eifel tower is 324 m. If it is made of iron, what will be the increase in length in cm, at 30^∘C?

d. Two substances A and B have specific heats c and 2 c respectively. If A and B are given Q and 4Q amounts of heat respectively, the change in their temperatures is the same. If the mass of A is m, what is the mass of B?

e. When a substance having mass 3 kg receives 600 cal of heat, its temperature increases by 10^∘C. What is the specific heat of the substance?

Q. In a steady state of thermal conduction, temperature of the ends

A

and

B

of a

20 cm

long rod are

100^{\circ} C

and

0^{\circ} C

, respectively. What will be the temperature of the rod at a point which is located at distance of

6 cm

from the end

A

of the rod?

Q. In a steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are

100^{\circ}

C and

0^{\circ}

C respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod

Q. Two identical rods A and B made up of iron and brass respectively are heated to the same temperature rise. The final length will be:

Join BYJU'S Learning Program

A bridge is made from 20 m long iron rods. At temperature 18∘C, the distance between two rods is 0.4 cm. Up to what temperature will the bridge be in good shape?

A bridge is made from $20$ m long iron rods. At temperature $18^{\circ} C$ , the distance between two rods is $0.4$ cm. Up to what temperature will the bridge be in good shape?