Question

Two rods A and B of identical dimensions are at
temperature 30°C. If A is heated upto
180°C and 'B' upto T°C then new lengths are
the same. If the ratio of the coefficient of linear
expansion of A and B is 4:3, then value of 'T' is​

Answer 1

Given :

Initial temperature = 30°C

Rod A is heated upto 180°C and rod B upto T°C.

Final length of both rods are same.

Ratio of coefficient of linear expansion = 4:3

To Find :

Final temperature of rod B$.$

Solution :

❖ Formula of change in length is given by

• ∆L = L × α × ∆T

» ∆L denotes change in length

» L denotes initial length

» α denotes coefficient of linear expansion

» ∆T denotes change in temperature

Change in length for both rods is same.

➙ ∆L for rod A = ∆L for rod B

➙ L × α₁ × ∆T₁ = L × α₂ × ∆T₂

• Both rods have same length at 30°C

➙ α₁ × ∆T₁ = α₂ × ∆T₂

➙ α₁ / α₂ = ∆T₂ / ∆T₁

➙ 4/3 = (T - 30) / (180 - 30)

➙ 4 × 150 = 3T - 90

➙ 600 + 90 = 3T

➙ T = 690/3

➙ T = 230 °C