Question

Two rods of same material have diameter in the ratio 1:2 and length is the ratio 2:1 if the temp difference between their ends is the same the ratio of heat conducted by them in a given time will be​

Answer 1

Answer:

The heat flow is given by:

Q

˙

=KA

dx

dT

=KA

l

ΔT

Given that ratio of diameters is 1:2, in other words the ratio of their areas (A∝D

2

)

is 1:4, and ratio of their lengths is 2:1.

The dimensions of the rod can be assumed to be:

Rod 1: length 2l, area A

Rod 2: length l, area 4A

Q

1

˙

=KA

2l

ΔT

Q

2

˙

=4KA

l

ΔT

Q

2

˙

Q

1

˙

=

8

1

Given that both have the same temperature difference across each other. For same time interval (T) the ratio of heat transfer will be

Q

2

Q

1

=

Q

2

˙

T

Q

1

˙

T

=

8

1