What is the temperature of the steel copper junction in the steady state of the system shown in the figure? Length of the steel rod =15 cm, length of the copper rod =10 cm, temperature of the furnace =300° C, temperature of the other end is 0° C. The area of cross-section of steel rod is twice that of copper rod. (Thermal conductivity of steel =50.2 Js -1 m -1 K -1 and of copper .=385 Js -1 m -1 K -1)

Question

What is the temperature of the steel copper junction in the steady state of the system shown in the figure? <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/8544392096de2379a74f39fef1e44f46-.png" /> Length of the steel rod =15 cm, length of the copper rod =10 cm, temperature of the furnace =300° C, temperature of the other end is 0° C. The area of cross-section of steel rod is twice that of copper rod. (Thermal conductivity of steel =50.2 Js -1 m -1 K -1 and of copper .=385 Js -1 m -1 K -1) (A) 36.6° C (B) 44.4° C (C) 92.5° C (D) 118.6° C

Tardigrade Admin · Accepted Answer

1= steel, 2= copper (K1 A1(300-T)/L1)=(K2 A2(T-0)/L2) ((50.2)(2 A2)(300-T)/15)=(385 A2 ⋅ T/10) ⇒ T=44.4° C

$36. 6^{\circ} C$

$44. 4^{\circ} C$

$92. 5^{\circ} C$

$118. 6^{\circ} C$

$1 =$ steel, $2 =$ copper
$\frac{K _{1} A _{1} ( 300 - T )}{L _{1}} = \frac{K _{2} A _{2} ( T - 0 )}{L _{2}}$
$\frac{( 50.2 ) ( 2 A _{2} ) ( 300 - T )}{15} = \frac{385 A _{2} \cdot T}{10}$
$\Rightarrow T = 44. 4^{\circ} C$

36.6∘C

44.4∘C

92.5∘C

118.6∘C

1= steel, 2= copper L1​K1​A1​(300−T)​=L2​K2​A2​(T−0)​ 15(50.2)(2A2​)(300−T)​=10385A2​⋅T​ ⇒T=44.4∘C

$36. 6^{\circ} C$

$44. 4^{\circ} C$

$92. 5^{\circ} C$

$118. 6^{\circ} C$

$1 =$ steel, $2 =$ copper
$\frac{K _{1} A _{1} ( 300 - T )}{L _{1}} = \frac{K _{2} A _{2} ( T - 0 )}{L _{2}}$
$\frac{( 50.2 ) ( 2 A _{2} ) ( 300 - T )}{15} = \frac{385 A _{2} \cdot T}{10}$
$\Rightarrow T = 44. 4^{\circ} C$