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A 1 kg mass of water held in a container is left in sunlight, so it becomes warmer than its surroundings. Sunlight delivers an average power of 700 W m⁻², and this is absorbed by the water over an effective area of 0.05 m². If heat loss to the surroundings obeys Newton's law of cooling, what is the steady-state temperature difference (in deg C) between the water and the surroundings after a long time? (Neglect the container; cooling constant = 0.001 s⁻¹, specific heat capacity of water = 4200 J kg⁻¹ K⁻¹.)
- 8.33
- 4.17
- 16.67
- 2.08
Correct answer: 8.33
Solution
At steady state the absorbed solar power exactly balances the heat radiated/lost to the surroundings, so the temperature stops rising and a constant difference is maintained.
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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