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A hollow and solid rod are made of same material. The length of each rod is 20cm and radius is 2cm. If their temperature is increase by 50Celcius,then their expension ratio Ea:Eb is​

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11th

Physics

Thermal Properties of Matter

Conduction

The lengths and radii of tw...

PHYSICS

The lengths and radii of two rods made of same material are in the ratios 1:2 and 2:3 respectively. If the temperature difference between the ends for the two rods be the same, then in the steady state, the amount of heat flowing per second through them will be in the ratio :

January 17, 2020

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Humaira Gayathri

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ANSWER

The rate of heat flow in a rod of length l , is given by ,

Q/t=KAΔθ/l ,

where A= cross- sectional area of rod ,

K= thermal conductivity of material of rod ,

Δθ= temperature difference between two ends of rod ,

now given that ratio of lengths of two rods =1:2 ,

let their lengths are l

1

=L , and l

2

=2L respectively ,

and given that ratio of radii of two rods =2:3 ,

let their radii are r

1

=2r , and r

2

=3r respectively ,

hence , their cross-sectional areas are A

1

=2π(2r)

2

and A

2

=2π(3r)

2

,

therefore , rate of heat flow in a rod of length L is ,

X=Q/t=K2π(2r)

2

Δθ/L , ...........eq1

and rate of heat flow in a rod of length 2L is ,

Y=Q

′

/t=K2π(3r)

2

Δθ/2L , ...........eq2 ,

dividing eq1 by eq2 ,

X/Y=(K2π(2r)

2

Δθ/L)/(K2π(3r)

2

Δθ/2L)=8:9 ,