The difference in length between a brass and an iron is 14CM at 10°C what must be the length of the iron for this difference to remain 14CM when both rods are heated to 100°C? Given that Linear expansivity of brass is 19 × 10^-6/K and lenear expansivity of iron is 12×10^-6/K

Answer 1

L1=L2

Answer 2

I need the solution

About the above questions

Answer 3

The difference in length between a brass and an iron is 14CM at 10°C what must be the length of the iron for this difference to remain 14CM when both rods are heated to 100°C? Given that Linear expansivity of brass is 19 × 10^-6/K and lenear expansivity of iron is 12×10^-6/K

Answer 4

0.38

Answer 5

*Solution✍🏼*😄
Let length of brass be *a*
Length of iron be *b*

All length above are at 10°c

✍🏼Their differences is 14cm
a-b=14...(i)

*In equation (i) above is (a-b) because brass expands faster than iron*😊😊

✍🏼At 100°c means change in temperature is 90°c

From ΔL=αΔθ×L

For brass
ΔL=α1Δθ×a.....(ii)

For iron
ΔL=α1Δθ×b....(iii)
Take equation (ii)=(iii) Now🥸 why?
*be cause difference in length to remain the same*

αΔθ×b=αΔθ×a
19×10-⁶a×90°=12×10-⁶×90°×b
19a=12b
a=(12/19)b.....(iv)
Take equation (iv) into equation (i)

a-b=14
(12/19)b-b=14
12b-19b=266
'7b=266
divide by 7 both sides u get

b=-38cm correct answer but negative

Therefore the length of iron is 38cm

Answer 6

Thanks alot for that solution .but why the answer bring us the negative sign

Answer 7

The answer is negative because when the temperature apply, it should be the length to increase but the length remain unchanged so it must occur negative length to show that the length is oppose the reality

Answer 8

It's not clear indeed...

Answer 9

38cm