Question

7. The coefficient of volume expansion of brass is 54 x 10^-6 /°C and coefficient of areal expansion of iron is 40/3 ×10^-6 /°F .If theyshow same difference in lengths at alltemperatures then their lengths are in the ratio ? ​

Answer 1

Hey Dear,

◆ Answer -

lb : li = 2 : 3

● Explaination -

# Given -

βi = 40/3×10^-6 /°F = 24×10^-6 /℃

γb = 54×10^-6 /℃

# Solution -

Various coefficients of expansions are related to each other as -

α = β/2 = γ/3

For brass,

αb = γb / 3

αb = 54×10^-6 / 3

αb = 18×10^-6 /℃

For iron,

αi = βi / 2

αi = 24×10^-6 / 2

αi = 12×10^-6 /℃

Given that changs in lengths is equal for both brass & iron.

∆lb = ∆li

αb.lb.ΔT = αi.li.ΔT

lb/li = αi/αb

Now substitute values,

lb/li = 12×10^-6 / 18×10^-6

lb/li = 2/3

Therefore, ratio of lengths of brass & iron wire is 2 : 3.

Thanks dear...

Answer 2

Answer:co efficient of cubical expansion of brass and iron are 54×10-6 /•c and 36×10-6/•c,

Explanation: