Exams › JEE Advanced › Physics
A rod enclosed in a thermally insulating sheath has its two ends maintained at temperatures T1 and T2. It is made of two joined sections of lengths l1 and l2 with thermal conductivities x1 and x2 respectively (the T1 end is the l1 section). In steady state, find the temperature at the junction (interface) of the two sections.
- (x1*l2*T1 + x2*l1*T2)/(x1*l2 + x2*l1)
- (x1*l1*T1 + x2*l2*T2)/(x1*l1 + x2*l2)
- (x1*T1 + x2*T2)/(x1 + x2)
- (l1*T1 + l2*T2)/(l1 + l2)
Correct answer: (x1*l2*T1 + x2*l1*T2)/(x1*l2 + x2*l1)
Solution
Equating the steady-state heat current through the two series sections and solving for the junction temperature T gives T = (x1*l2*T1 + x2*l1*T2)/(x1*l2 + x2*l1).
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 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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