(A) Let the junction temperature be $T \,K$. In the steady state, the rate of heat flow is the same through both rods.Using the formula for heat condu

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(A) Let the junction temperature be $T \,K$. In the steady state, the rate of heat flow is the same through both rods.Using the formula for heat conduction, $\frac{Q}{t} = \frac{kA(T_2 - T_1)}{l}$, we have:$\frac{Q}{t} = \frac{k_{steel} A (500 - T)}{2} = \frac{k_{Al} A (T - 300)}{1}$Since the cross-sectional areas $A$ are the same, we can cancel them out:$\frac{50(500 - T)}{2} = \frac{200(T - 300)}{1}$$25(500 - T) = 200(T - 300)$$12500 - 25T = 200T - 60000$$225T = 72500$$T = \frac{72500}{225} \approx 322.2 \,K$Thus, the junction temperature is approximately $322 \,K$.

Class 11 Physics 2 Thermal Properties of Matter: Heat Transfer Heat Conduction and Thermal Conductivity

Medium

An aluminium rod of length $1 \,m$ and a steel rod of length $2 \,m$, both having the same cross-sectional area, are soldered together end-to-end. The thermal conductivity of the aluminium rod and the steel rod is $200 \,Js^{-1} \,m^{-1} \,K^{-1}$ and $50 \,Js^{-1} \,m^{-1} \,K^{-1}$ respectively. The temperatures of the free ends are maintained at $300 \,K$ and $500 \,K$. What is the temperature of the junction (in $\,K$)?

TS EAMCET 2018 All TS EAMCET

A
$322$
B
$350$
C
$367$
D
$400$

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2 Thermal Properties of Matter: Heat Transfer

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$Assertion :$ $A$ brass tumbler feels much colder than a wooden tray on a chilly day.
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