Question

A Brass rod of length 0.40 m and steel rod of length 0.60 m, both are initially at 0oC are heated to 750C. If the increase in lengths is the same for both the rods, calculate the linear expansivity of brass. The linear expansivity of steel is 12x10-6 oC -1 .

Answer 1

Answer:

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Explanation:

A Brass rod of length 0.40 m and steel rod of length 0.60 m, both are initially at 0oC are heated to 750C. If the increase in lengths is the same for both the rods, calculate the linear expansivity of brass. The linear expansivity of steel is 12x10-6 oC -1 .

Answer 2

Given info : A Brass rod of length 0.40 m and steel rod of length 0.60 m, both are initially at 0°C are heated to 75°C. the linear expansion of steel is 12 × 10¯⁶/°C

To find : if the increase in lengths is the same for both the rods, calculate the linear expansion of brass.

solution : case 1 : change in length of steel bar, ∆l = l₀α∆T

here, initial length of steel bar, l₀ = 0.60 m

coefficient of linear expansion, α = 12 × 10¯⁶/°C

change in temperature, ∆T = 75°C

so, ∆l = 0.6 × 12 × 10¯⁶ × 75 m .....(1)

case 2 : change in length of brass bar, ∆l = l₀'α'∆T

here, initial length of steel bar, l₀ = 0.40 m

coefficient of linear expansion = α'

change in temperature, ∆T = 75°C

so, ∆l = 0.4 × α' × 75 .....(2)

from equations (1) and (2) we get,

0.6 × 12 × 10¯⁶ × 75 = 0.4 × α' × 75

⇒18 × 10¯⁶/°C = α'

Therefore the coefficient of linear expansion of brass is 18 × 10¯⁶/°C