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Several identical rods, each of thermal conductance K and cross-sectional area A, form a symmetric network in which the rods AB, AO and AD branch out from corner A and recombine toward corner C. The ends A and C are held at temperatures 2*T0 and T0 respectively. By the symmetry of the network, which of the following statements is correct?
- The rate of heat flow through AB, AO and AD is the same
- The rate of heat flow through BO and OD is different
- The temperature at junction B differs from that at junction D
- No heat flows from A to C
Correct answer: The rate of heat flow through AB, AO and AD is the same
Solution
Because the three branches from A are symmetric and identical, they each carry an equal share of the total heat current, and the symmetric junctions reach the same temperature. Thus the equal-flow statement is correct, while the statements claiming asymmetry are false, and heat clearly flows since 2*T0 > T0.
Related JEE Advanced Physics questions
- Match the temperature of a blackbody listed in Group-I to the corresponding statement in Group-II, and select the correct answer.
[Given: Wien’s constant = 2.9 × 10⁻³ m-K and hc/e = 1.24 × 10⁻⁶ V-m]
Group-I:
(P) 2000 K
(Q) 3000 K
(R) 5000 K
(S) 10000 K
Group-II:
(1) The peak wavelength of emitted radiation can cause photoelectron ejection from a metal with a work function of 4 eV.
(2) The peak wavelength of emitted radiation falls within the visible spectrum.
(3) The peak wavelength of emitted radiation produces the broadest central diffraction maximum in a single-slit setup.
(4) The energy radiated per unit area is one-sixteenth of that emitted by a blackbody at 6000 K.
(5) The peak wavelength of emitted radiation is suitable for imaging human bones.
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- A steel rail track of length 1 km was laid at an ambient temperature of 20 deg C with no gaps for thermal expansion. When the temperature rose to 25 deg C, the track buckled and formed an isosceles triangle shape. Given the coefficient of linear expansion of steel is 14 * 10⁻⁶ per K, find the height of the buckle in metres (to the nearest integer).
- Two rods are connected end to end. Rod 1 has length l and thermal conductivity 2K. Rod 2 has length 2l and thermal conductivity K. Both rods have the same cross-sectional area. What is the effective thermal conductivity of the combination?
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- A continuous-flow calorimeter is used in two separate experiments to find the specific heat of a liquid. In the first trial, supplying 60 W raises the liquid temperature by 10 K. In the second trial, the power is doubled to 120 W, but the same 10 K rise is maintained by tripling the flow rate. Assuming heat loss to surroundings is the same in both trials, what is the power lost to the surroundings?
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