### What should be the lengths of an aluminium and a brass rods at STP.so that brass rod is longer than the aluminium rod by 4cm at all conditions of temperature.(alpha alumn 24exp -6 brass 20 expo -6c

**Data :**

Let Length of aluminum = La Length of brass = Lb =La + 0.04 (In meters) α for aluminum= 24x10 -6 c-1 α for brass= 20 x10 -6 c-1 Lengths at 0 0C La’ = ? and Lb’=?

**Solution:**

Length of aluminum is given by La’=La ( 1 + α Δt)----------------1 Lb’=Lb ( 1 + α Δt)-----------------2 Subtracting eq(1) from eq(2), we get La’ - Lb’ =La ( 1 + α Δt) - Lb ( 1 + α Δt) = La + La α Δt) - Lb + Lb α Δt =(La – Lb )+ Δt (La α - Lb α) 0.04 =0.04 + Δt (La α - Lb α) So Δt (La α - Lb α) =0 Since La α = Lb α La x 24x10 -6 = Lb x20 x10 -6 La =(20 /24) x Lb =20 Lb / 24 ------------3 Since Lb =La + 0.04 Putting value of La from eq (3) , we get Lb =(20 Lb / 24) +0.04or 24 x (Lb -0.04)=20 Lb 24 Lb – 20 Lb =0.96or Lb= 0.96/4 =

**Lb=0.24 m Answer**Now La= 0.24 -0.04 =

**0.02 m Answer**