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Two rods of equal length and diameter ha...

Two rods of equal length and diameter have thermal conductivite 3 and 4 units respectively. If they are joined in series, the thermal conductivity of the combination in the given units would be

A

`3.43`

B

7

C

`7.34`

D

`6.25`

Text Solution

Verified by Experts

The correct Answer is:
A
Thermal resisitance of a rod `R= (L )/(KA)`
where L is the length of a rod K , is the thermal conductivity of the material of the rod and A is the area of cross - section of a rod .
here `L_1 = L_2 - L ,A_1 = A_2 = A , K_1 = 3 ` unit `K_2 = 4 ` unit Let the thermal resistance of the two rods are `R_1 ` and` R_2` respectively .As the rods are joined in series
` therefore R_s = R_1 +R_2`
` R_s =R_1 +R_2`
` R_s =(L_1)/( K_1A_1 ) +(L_2)/(K_2 A_2) =(L )/(K_1 A ) +(L )/(K_2A )`
`R_s =((1)/(K_1 )+(1)/(K_2)) (L)/(A)`
LEt K be equivalent thermal conductivity
` therefore R_s = (L_1 +L_2)/(KA) =(2L )/( KA)`
from eq (i ) and (ii ) we get
` (2)/(K ) =(1)/(K_1) +(1)/(K_2) or K=( 2K_1 K_2)/(K_1 +K_2)`
`or K = ( 2 xx 3xx 4 )/( 3 +4 ) = 3.428 =3.43`
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