Class 11 NEET Physics Properties of Matter Questions

The amount of heat flows in time t through a cylindrical metallic rod of length L and uniform area of cross-section A(=πR2) with its ends maintained at temperatures T1 and T2(T1>T2) is given by
Q=

KA(T1−T2)t

L

......(i)
where AT is the thermal conductivity of the material of the rod
Area of cross-section of new rod A′=π(

R

2

)2
=

πR2

4

=

A

4

....(ii)
As the volume of the rod remains unchanged
∴AL=A′L′
where L′ is the length the new rod
or L′=L

A

A′

...........(iii)
=4L (Using (ii))
Now, the amount of heat flows in same time t in the new rod with its ends maintained at the same temperatures T1 and T2 is given by Q′=

KA′(T1−T2)t

L′

..........(iv)
Substituting the values of A′ and L′ from equations (ii) and (iii) in the above equation, we get

=

1

16

Q (Using (i))