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A metal block is placed in a room at 10 deg C. It is heated by an electric heater of power 500 W until its temperature reaches 50 deg C. The initial rate of rise of temperature is 2.5 deg C/sec. The heater is switched off; a 100 W heater is then required to maintain the block at 50 deg C. Assuming Newton's Law of Cooling is valid, which of the following statements are correct? (A) The heat capacity of the block is 200 J/K. (B) The rate of cooling of the block at 50 deg C, if the 100 W heater is also switched off, is 1 K/sec. (C) The heat radiated per second when the block is at 30 deg C is 100 J/sec. (D) The heat radiated per second when the block is at 30 deg C is 50 J/sec.
- The heat capacity of the block is 200 J/K.
- The rate of cooling of the block at 50 deg C if the 100 W heater is also switched off is 1 K/sec.
- The heat radiated per second is 100 J/sec when the block is at 30 deg C.
- The heat radiated per second is 50 J/sec when the block is at 30 deg C.
Correct answer: The heat capacity of the block is 200 J/K.
Solution
At t=0, the block is at room temperature (10 deg C), so heat loss = 0. All 500 W heats the block: C = P/(dT/dt) = 500/2.5 = 200 J/K (A is correct). To maintain 50 deg C, heat loss = 100 W; by Newton's law, k = 100/(50-10) = 2.5 W/K. If 100 W heater is switched off, rate of cooling = 100 W / 200 J/K = 0.5 K/sec (B is wrong). At 30 deg C: heat loss = 2.5*(30-10) = 50 J/sec (D is correct, C is wrong).
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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