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Three rods of identical geometrical dimensions are connected as shown. In arrangement (a) two aluminium rods and one copper rod are used, and in arrangement (b) the same three rods are reconnected, with the temperature difference across the ends kept the same. The thermal conductivities of aluminium and copper are 200 W/m-deg C and 400 W/m-deg C. What is the ratio of the rate of heat flow in arrangement (a) to that in arrangement (b)?
- 3: 16
- 16: 3
- 3: 8
- 8: 3
Correct answer: 3: 16
Solution
Each rod has the same A, L and end temperature difference, so the rate of heat flow is proportional to the effective thermal conductance of the arrangement. In arrangement (a) the rods form a series path so the effective conductance is small; in arrangement (b) the same rods form a parallel path so the effective conductance is large. Putting K_Al = 200 and K_Cu = 400 and forming the series-versus-parallel effective conductances for the two-aluminium-one-copper network gives the ratio of heat-flow rates as 3: 16.
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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