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 A 2 respectively. If the rate of heat conduction in 1 is four times that in 2, then :

Question

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 A 2 respectively. If the rate of heat conduction in 1 is four times that in 2, then : (A)  K 1A1 = 4K2A2 (B)  K1A1= 2K2A2 (C)  4K1A1= K2A2 (D)  K1A1= K2A2

Tardigrade Admin · Accepted Answer

(a): Let L be length of each rod.
Rate of heat flow in rod 1 for the temperature
difference

Δ T

is

H_{1} = \frac{K _{1} A _{1} Δ T}{L}

Rate of heat flow in rod 2 for the same difference

Δ T

is

H_{2} = \frac{K _{2} A _{2} Δ T}{L}

As per question

H_{1} = 4 H_{2}

\frac{K _{1} A _{1} Δ T}{L} = 4 \frac{K _{2} A _{2} Δ T}{L}

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

Q. 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 :

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

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

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

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

Q. 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 :

K1​A1​=4K2​A2​

K1​A1​=2K2​A2​

4K1​A1​=K2​A2​

K1​A1​=K2​A2​

(a): Let L be length of each rod. Rate of heat flow in rod 1 for the temperature difference ΔT is H1​=LK1​A1​ΔT​ Rate of heat flow in rod 2 for the same difference ΔT is H2​=LK2​A2​ΔT​ As per question H1​=4H2​ LK1​A1​ΔT​=4LK2​A2​ΔT​ K1​A1​=4K2​A2​

Q. 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 :

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

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

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

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