Question 604: Thermodynamics & KTG

Question

A rod CD of thermal resistance 10.0 KW$$-$$1 is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at 200$$^\circ$$C, 100$$^\circ$$C and 125$$^\circ$$C respectively. The heat current in CD is P watt. The value of P is ................. .

Accepted Answer

Rods are identical so
R
AB
= R
CD
= 10 Kw
$$-$$1
C is mid-point of AB, so
R
AC
= R
CB
= 5 Kw
$$-$$1
at point C
$${{200 - T} \over 5} = {{T - 125} \over {10}} + {{T - 100} \over 5}$$
2(200 $$-$$ T) = T $$-$$ 125 + 2(T $$-$$ 100)
400 $$-$$ 2T = T $$-$$ 125 + 2T $$-$$ 200
$$T = {{725} \over 5}$$ = 145$$^\circ$$C
$${I_h} = {{145 - 125} \over {10}}w = {{20} \over {10}}w$$
I
h
= 2w

Thermodynamics & KTG

A rod CD of thermal resistance 10.0 KW$-1 is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at 200^\circC, 100^\circC and 125^\circ$C respectively. The heat current in CD is P watt. The value of P is ................. .

Choose the correct answer: