Two rods of same lengths, radius and material transfer a given amount heat in $12 s$ . When they are joined as shown in the (Fig 1). But when they are joined as shown in the (Fig.2), then they will transfer same heat in same conditions in.

24 s

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13 s

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15 s

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48 s

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Solution

The correct option is D $48 s$
Heat $Q = K A \frac{Δ θ}{l} t$
For same heat, conductivity , $t \propto \frac{l}{A}$
$\frac{t_{1}}{t_{2}} = \frac{l_{1} A_{2}}{l_{2} A_{1}}$
Now $A_{2} = \frac{A_{1}}{2} & l_{2} = 2 l_{1}$
$t_{1} = 12 s, ∴ t_{2} = 4 t_{1} = 48 s$

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Two rods of same lengths, radius and material transfer a given amount heat in 12s. When they are joined as shown in the (Fig 1). But when they are joined as shown in the (Fig.2), then they will transfer same heat in same conditions in.

The correct option is D 48 sHeat Q=KAΔθltFor same heat, conductivity , t∝lAt1t2=l1A2l2A1Now A2=A12&l2=2l1t1=12s,∴t2=4t1=48s

Two rods of same lengths, radius and material transfer a given amount heat in $12 s$ . When they are joined as shown in the (Fig 1). But when they are joined as shown in the (Fig.2), then they will transfer same heat in same conditions in.

The correct option is D $48 s$
Heat $Q = K A \frac{Δ θ}{l} t$
For same heat, conductivity , $t \propto \frac{l}{A}$
$\frac{t_{1}}{t_{2}} = \frac{l_{1} A_{2}}{l_{2} A_{1}}$
Now $A_{2} = \frac{A_{1}}{2} & l_{2} = 2 l_{1}$
$t_{1} = 12 s, ∴ t_{2} = 4 t_{1} = 48 s$