Question 420: Thermodynamics & KTG

Question

Temperature difference of 120
o
C is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length $${{3L} \over 2},$$ is connected across AB  (see figure). In steady state, temperature difference between P and Q will be  close to :

Accepted Answer

We know,
Resistance, R = $${{ho L} \over A}$$
$$ 	herefore $$   R $$ \propto $$ L
So, Resistance is directly proportional to lengt5h of the rod.
Equivalent resistance between A and B is,
R
eq
=  $${R \over 2} + {{R 	imes {{3R} \over 2}} \over {R + {{3R} \over 2}}} + {R \over 2}$$
=  R + $${{3{R^2}} \over 2} 	imes {2 \over {5R}}$$
= R + $${{3R} \over 5}$$
= $${{8R} \over 5}$$
Thermal current between point A and B is,
I = $${{\Delta {T_{AB}}} \over {{{\mathop{m R}
olimits} _{eq}}}}$$
=  $${{120 - 0} \over {{{8R} \over 5}}}$$
=   $${{120 	imes 5} \over {8R}}$$
Resistance between P and Q = $${{3R} \over 5}$$
$$ 	herefore $$   $$\Delta $$T
PQ
= $${m I} 	imes {{3R} \over 5}$$
=  $${{120 	imes 5} \over {8R}} 	imes {{3R} \over 5}$$
= 45
o
C

Answer

45
o
C

Answer

75
o
C

Answer

60
o
C

Answer

35
o
C

Thermodynamics & KTG

Temperature difference of 120 o C is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length ${{3L} \over 2},$ is connected across AB (see figure). In steady state, temperature difference between P and Q will be close to :

Choose the correct answer: