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Standard XII

Physics

Thermal Resistance

Two metal rod...

Question

Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_{1}$ and $K_{2}$ and cross sectional areas $A_{1}$ and $A_{2}$ , respectively. If the rate of heat conduction in $1$ is four times that in $2$ , then

K_{1} A_{1} = K_{2} A_{2}

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K_{1} A_{1} = 4 K_{2} A_{2}

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K_{1} A_{1} = 2 K_{2} A_{2}

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4 K_{1} A_{1} = K_{2} A_{2}

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Solution

The correct option is B $K_{1} A_{1} = 4 K_{2} A_{2}$
The relation is as follows:

$\frac{Q}{T} = \frac{K A Δ T}{d}$

$∵ {(\frac{Q}{T})}_{1} = 4 {(\frac{Q}{T})}_{2}$

$\frac{K_{1} A_{1} Δ T}{d} = 4 \frac{K_{2} A_{2} Δ T}{d}$

$K_{1} A_{1} = 4 K_{2} A_{2}$
Hence (b) is the correct option.

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Two metal rods 1 and 2 of same lengths have same temperature difference between their ends. Their thermal conductivities are K1 and K2 and cross sectional areas A1 and A2, respectively. If the rate of heat conduction in 1 is four times that in 2, then

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Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_{1}$ and $K_{2}$ and cross sectional areas $A_{1}$ and $A_{2}$ , respectively. If the rate of heat conduction in $1$ is four times that in $2$ , then

The correct option is B $K_{1} A_{1} = 4 K_{2} A_{2}$
The relation is as follows:

$\frac{Q}{T} = \frac{K A Δ T}{d}$

$∵ {(\frac{Q}{T})}_{1} = 4 {(\frac{Q}{T})}_{2}$

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$K_{1} A_{1} = 4 K_{2} A_{2}$
Hence (b) is the correct option.