Question

Before heating the rods, the length of the rods were: Iron rod = 1.5m, Copper rod = 1.5m. Both rods are heated for 1 hour, with the same amount of heat. What is the length of the rods, after 1 hour? ​

Answer 1

Explanation:

Let Ls and Lc be the lengths of the steel and copper rods and αs and αc be their coefficients of linear expansion respectively. When the rods are heated by △t∘C, the increase in length of steel rod and copper rod are

△Ls=Lsαs△t

△Lc=Lcαc△t

Given Ls−Lc=5 cm for all △t.

Lsαs△t=Lcαc△t

LcLs=αsαc=1.1×10−51.7×10−5

Ls=1117Lc. Using this in Ls−

Answer 2

Answer:

Let L

s

and L

c

be the lengths of the steel and copper rods and α

s

and α

c

be their coefficients of linear expansion respectively. When the rods are heated by △t

∘

C, the increase in length of steel rod and copper rod are

△L

s

=L

s

α

s

△t

△L

c

=L

c

α

c

△t

Given L

s

−L

c

=5 cm for all △t.

L

s

α

s

△t=L

c

α

c

△t

L

c

L

s

=

α

s

α

c

=

1.1×10

−5

1.7×10

−5

L

s

=

11

17L

c

. Using this in L

s

−L

c

=5 and solving, we get L

c

=9.17 cm

Therefore, L

s

=5+9.17=14.17