Two rods P and Q of equal lengths have thermal conductivities K1 and K2 and cross-sectional areas A1 and A2 respectively. If the temperature difference across the ends of each rod is the same, then the condition for which the rate of flow of heat through each of them will be equal, is

Question

Two rods P and Q of equal lengths have thermal conductivities K1 and K2 and cross-sectional areas A1 and A2 respectively. If the temperature difference across the ends of each rod is the same, then the condition for which the rate of flow of heat through each of them will be equal, is (A) (A1/A2)=(K2/K1) (B) (A1/A2)=(K1/K2) (C) (A1/A2)= √(K1/K2)  (D) (A1/A2)=( (K2/K1))2

Tardigrade Admin · Accepted Answer

((Δ Q/Δ t))P=((Δ Q/Δ t))Q K1A1((T1 - T2)/l)=K2A2((T1 - T2)/l) Or K1A1=K2A2 or (A1/A2)=(K2/K1)

$\frac{A _{1}}{A _{2}} = \frac{K _{2}}{K _{1}}$

$\frac{A _{1}}{A _{2}} = \frac{K _{1}}{K _{2}}$

$\frac{A _{1}}{A _{2}} = \frac{K _{1}}{K _{2}}$

$\frac{A _{1}}{A _{2}} = (\frac{K _{2}}{K _{1}})^{2}$

$(\frac{Δ Q}{Δ t})_{P} = (\frac{Δ Q}{Δ t})_{Q}$
$K_{1} A_{1} \frac{( T _{1} - T _{2} )}{l} = K_{2} A_{2} \frac{( T _{1} - T _{2} )}{l}$
Or $K_{1} A_{1} = K_{2} A_{2}$ or $\frac{A _{1}}{A _{2}} = \frac{K _{2}}{K _{1}}$

A2​A1​​=K1​K2​​

A2​A1​​=K2​K1​​

A2​A1​​=K2​K1​​​

A2​A1​​=(K1​K2​​)2

(ΔtΔQ​)P​=(ΔtΔQ​)Q​ K1​A1​l(T1​−T2​)​=K2​A2​l(T1​−T2​)​ Or K1​A1​=K2​A2​ or A2​A1​​=K1​K2​​

$\frac{A _{1}}{A _{2}} = \frac{K _{2}}{K _{1}}$

$\frac{A _{1}}{A _{2}} = \frac{K _{1}}{K _{2}}$

$\frac{A _{1}}{A _{2}} = \frac{K _{1}}{K _{2}}$

$\frac{A _{1}}{A _{2}} = (\frac{K _{2}}{K _{1}})^{2}$

$(\frac{Δ Q}{Δ t})_{P} = (\frac{Δ Q}{Δ t})_{Q}$
$K_{1} A_{1} \frac{( T _{1} - T _{2} )}{l} = K_{2} A_{2} \frac{( T _{1} - T _{2} )}{l}$
Or $K_{1} A_{1} = K_{2} A_{2}$ or $\frac{A _{1}}{A _{2}} = \frac{K _{2}}{K _{1}}$