JEE Physics Thermal Properties Of Matter MCQs Set 26

Answer: (b) Q_B is maximum

Explanation:
1. \( T\propto\frac1{\lambda_m} \) and \( Q\propto r^2T^4\propto\frac{r^2}{\lambda_m^4} \).
2. Taking λ in hundreds of nm: A gives 4/3⁴ = 0.049, B gives 16/4⁴ = 0.0625, C gives 36/5⁴ = 0.0576. So Q_B is the largest.

Teacher's Note:
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Answer: (a) \( 0.6\,\sigma AT^4 \)

Explanation:
1. Radiated power \( =e\sigma AT^4 \).
2. With e = 0.6 the rate is 0.6σAT⁴.

Teacher's Note:
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Answer: (b) 0.605 kg

Explanation:
1. Area = 6 × 0.5² = 1.5 m². Rate = 0.05 × 1.5 × 30/0.04 = 56.25 W.
2. Energy per hour = 56.25 × 3600 = 2.025 × 10⁵ J, so mass = 2.025 × 10⁵/3.34 × 10⁵ ≈ 0.606 kg.

Teacher's Note:
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Answer: (d) 284

Explanation:
1. Curved area \( =2\pi rh=2\pi\times30\times100=1.885\times10^4 \) cm².
2. \( \frac{KA\Delta T}{d}=\frac{9\times10^{-5}\times1.885\times10^4\times40}{1}=67.9 \) cal/s ≈ 285 W.

Teacher's Note:
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Answer: (d) 0.65 s

Explanation:
1. Rate \( =\frac{0.92\times800\times100}{0.3}=2.45\times10^5 \) cal/s.
2. Heat to melt the ice = 2000 × 80 = 1.6 × 10⁵ cal, so t = 0.65 s.

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Answer: (b) 0.69

Explanation:
1. Wien's law: \( T\propto\frac1{\lambda_m} \).
2. \( \frac{T_{sun}}{T_{star}}=\frac{350}{510}=0.686\approx0.69 \).

Teacher's Note:
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Answer: (c) \( K_3=\frac{K_1K_2}{K_1+K_2} \)

Explanation:
1. Path PRQ is two rods in series: resistance \( \frac L{K_1A}+\frac L{K_2A} \). Path PQ resistance \( \frac L{K_3A} \).
2. Equal rates need \( \frac1{K_3}=\frac1{K_1}+\frac1{K_2}\Rightarrow K_3=\frac{K_1K_2}{K_1+K_2} \).

Teacher's Note:
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Answer: (a) \( \frac{r_1r_2}{r_2-r_1} \)

Explanation:
1. For a thin shell: \( dQ=-4\pi K r^2\frac{dT}{dr} \). Integrating from r₁ to r₂:
2. \( Q=\frac{4\pi Kr_1r_2(T_1-T_2)}{r_2-r_1} \), so it is proportional to \( \frac{r_1r_2}{r_2-r_1} \).

Teacher's Note:
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Answer: (a) 20860 cal

Explanation:
1. Heat absorbed in 2 min = 59 × 8 = 472 cal, so 236 cal per minute by the mirror area π × 6² = 113.1 cm².
2. Per m² (10⁴ cm²): 236 × 10⁴/113.1 ≈ 20866 cal.

Teacher's Note:
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Answer: (a) 1 and 2 only

Explanation:
1. Conduction passes through a material and convection through a moving fluid.
2. Radiation travels through vacuum and needs no medium.

Teacher's Note:
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Answer: (b) 2 and 4

Explanation:
1. Every body emits and absorbs radiation at all times; a net loss or gain depends on the temperatures.
2. At T the emission and absorption are equal (dynamic equilibrium), so statements 2 and 4 are correct.

Teacher's Note:
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Every body above absolute zero emits radiation, so the body radiates even though it is colder than the room.
2. The reason explains the assertion.

Teacher's Note:
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. By Stefan's law the radiated power is proportional to T⁴, so doubling T gives 16 times: assertion true.
2. The specific heat varies with temperature, which is true, but it is not the reason.

Teacher's Note:
1. T
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Answer: (c) A is true, but R is false.

Explanation:
1. The assertion is true because water has a high specific heat capacity.
2. Water is actually a poor conductor of heat, so the reason is false.

Teacher's Note:
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Every body above 0 K radiates: true. Stefan's law gives the rate proportional to T⁴: true.
2. The T⁴ law does not explain why radiation takes place at all temperatures.

Teacher's Note:
1. T
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Wool traps air in its fibres, forming an insulating layer.
2. Air being a poor conductor reduces the loss of body heat.

Teacher's Note:
1. T
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Answer: (c) A is true, but R is false.

Explanation:
1. Wien's displacement law gives λ_m T = constant, so the peak shifts to shorter wavelengths: assertion true.
2. The peak wavelength is inversely proportional to T, not proportional to T⁴, so the reason is false.

Teacher's Note:
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Answer: (c) A is true, but R is false.

Explanation:
1. A small hole in a closed cavity at uniform temperature emits black body radiation: assertion true.
2. Metals in general are not black bodies (polished metals reflect), so the reason is false.

Teacher's Note:
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Blue light has a shorter wavelength than red light.
2. By Wien's law the hotter star has the shorter peak wavelength.

Teacher's Note:
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