First slide

Heat transfer

Question

Figure shows a conductor rod of non uniform cross- section. The ends of the rod are maintained at constant temperatures $100^{\circ} C$ and $0^{\circ} C$ respectively. At steady state, temperatures of P, Q, R and S are $T_{P}, T_{Q}, T_{R} and T_{S}$ respectively, then:

Moderate

A

$T_{P} - T_{Q} = T_{R} - T_{S}$
B

$T_{P} - T_{Q} > T_{R} - T_{S}$
C

$T_{P} - T_{Q} < T_{R} - T_{S}$
D

$T_{P} > 2 (T_{P} - T_{Q})$

Solution

Along length of conductor
$\frac{d Q}{d t} =$ constant
$\Rightarrow \frac{d Q}{d t} = K A \frac{d T}{d x} = constant$
$\Rightarrow A d T = constant$
$A_{P Q} > A_{R S}$
$A_{P Q} =$ Area of cross-section at point P
$A_{R S} =$ Area of cross-section at point R
$∴ {(Δ T)}_{P Q} < {(Δ T)}_{R S}$
Therefore, the correct answer is (C).

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