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Q. No.The radius of a spherical black body is \(R,\) and \(\alpha\) represents the rate of energy production within the body. The temperature of the given black body in a steady-state is: (where \(\sigma\) is Stefan- Boltzmann constant)
1.
\(\left(\dfrac{\alpha}{\sigma \times 4 \pi R^2}\right)^{\dfrac{1}{4}} \)
2.
\(\left(\dfrac{\sigma \times 4 \pi R^2}{\alpha}\right)^{\dfrac{1}{4}}\)
3.
\(\left(\dfrac{\alpha}{\sigma \times 4 \pi R^2}\right)\)
4.
\(\left(\dfrac{4 \pi R^2 \times \sigma}{\alpha}\right)\)
Subtopic: Stefan-Boltzmann Law |
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Level 1: 80%+
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Two bodies \(A\) and \(B\) have emissivities of \(e_{A}\) and \(e_{B}\) respectively. The outer surface areas of two bodies are equal. The two bodies emit total radiant power at the same rate. The ratio of wavelength of \(B\) corresponding to maximum spectral radiancy to that of wavelength of \(A\) corresponding to maximum spectral radiancy is:
| 1. | \(\left(\dfrac{e_B}{e_A}\right)^4\) | 2. | \(\left(\dfrac{e_A}{e_B}\right)^{1\over 2}\) |
| 3. | \(\left(\dfrac{e_B}{e_A}\right)^{1\over 4}\) | 4. | \(\left(\dfrac{e_A}{e_B}\right)^{1\over 4}\) |
Subtopic: Wien's Displacement Law |
57%
Level 3: 35%-60%
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Two metal rods \((1)\) and \((2)\) of the same length have the same temperature difference between their ends. Their thermal conductivities are \({K}_1\) and \({K}_2\) and cross-sectional areas \({A}_{1}\) and \({A}_{2},\) respectively. If the rate of heat conduction in \((1)\) is four times that in \((2),\) then:
| 1. | \(K_1 A_1=4K_2 {A}_2 \) | 2. | \(K_1 {A}_1=2 {K}_2 {A}_2 \) |
| 3. | \(4 {K}_1{A}_1={K}_2 {A}_2 \) | 4. | \({K}_1 {A}_1={K}_2 {A}_2\) |
Subtopic: Conduction |
74%
Level 2: 60%+
NEET - 2013
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The density of water at \(20^\circ \text{C}\) is \(998~\text{kg/m}^3\) and at \(40^\circ \text{C}\) is \(992~\text{kg/m}^3.\) The coefficient of volume expansion of water is:
1. \(3 \times 10^{-4} / ^\circ\text C\)
2. \(2 \times 10^{-4} / ^\circ\text C\)
3. \(6 \times 10^{-4} / ^\circ\text C\)
4. \(10^{-4} / ^\circ\text C\)
1. \(3 \times 10^{-4} / ^\circ\text C\)
2. \(2 \times 10^{-4} / ^\circ\text C\)
3. \(6 \times 10^{-4} / ^\circ\text C\)
4. \(10^{-4} / ^\circ\text C\)
Subtopic: Thermal Expansion |
73%
Level 2: 60%+
NEET - 2013
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The pressure that needs to be applied to the ends of a steel wire of length \(20~\text{cm}\) and area of cross-section \(0.5~\text m^2\) to keep its length constant when the temperature is raised by \(200^\circ \text{C}\) is:
(Young's modulus of elasticity \((Y)\) for steel is \(2\times10^{11}\) N/m2 and the coefficient of thermal expansion \((\alpha)\) is \(1.1\times10^{-5}~\text{K}^{-1})\)
(Young's modulus of elasticity \((Y)\) for steel is \(2\times10^{11}\) N/m2 and the coefficient of thermal expansion \((\alpha)\) is \(1.1\times10^{-5}~\text{K}^{-1})\)
| 1. | \(3.2 \times 10^6~\text{Pa}\) | 2. | \(2.2 \times 10^8~\text{Pa}\) |
| 3. | \(4.4 \times 10^8~\text{Pa}\) | 4. | \(2.2 \times 10^9~\text{Pa}\) |
Subtopic: Thermal Stress |
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Level 2: 60%+
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A pan filled with hot food cools from \(95^\circ \text{C}\) to \(85^\circ \text{C}\) in \(2\) min when the room temperature is \(20^\circ \text{C}.\) The time taken by the food to cool from \(55^\circ \text{C}\) to \(45^\circ \text{C}\) will be:
| 1. | \(260\) s | 2. | \(280\) s |
| 3. | \(300\) s | 4. | \(320\) s |
Subtopic: Newton's Law of Cooling |
80%
Level 1: 80%+
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The shapes of the black body radiation curves depend on their:
1. Masses
2. Surface areas
3. Materials
4. Temperatures
1. Masses
2. Surface areas
3. Materials
4. Temperatures
Subtopic: Radiation |
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Level 2: 60%+
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Two rods, one made of copper and the other made of steel, of the same length and same cross-sectional area are joined together. The thermal conductivity of copper and steel are \(385~\text{Js}^{-1}\text{K}^{-1}\text{m}^{-1}\) and \(50~\text{Js}^{-1}\text{K}^{-1}\text{m}^{-1}\) respectively. The free ends of copper and steel are held at \(100^\circ \text{C}\) and \(0^\circ \text{C}\) respectively. The temperature at the junction is, nearly:
1. \(12^\circ \text{C}\)
2. \(50^\circ \text{C}\)
3. \(73^\circ \text{C}\)
4. \(88.5^\circ \text{C}\)
1. \(12^\circ \text{C}\)
2. \(50^\circ \text{C}\)
3. \(73^\circ \text{C}\)
4. \(88.5^\circ \text{C}\)
Subtopic: Conduction |
74%
Level 2: 60%+
NEET - 2022
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Given that the coefficient of linear expansion of brass is \(\alpha=0.00002^\circ \text{C}^{-1},\) what rise in temperature is required to increase the length of a brass rod by \(1\text{%} \text{?}\)
1. \(750^\circ \text{C}\)
2. \(500^\circ \text{C}\)
3. \(200^\circ \text{C}\)
4. \(100^\circ \text{C}\)
1. \(750^\circ \text{C}\)
2. \(500^\circ \text{C}\)
3. \(200^\circ \text{C}\)
4. \(100^\circ \text{C}\)
Subtopic: Thermal Expansion |
87%
Level 1: 80%+
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In an experiment to verify Newton’s Law of Cooling, a graph is plotted between the temperature difference \((\Delta T)\) of water and its surroundings and time, as shown in the figure. The initial temperature of the water is \(80^\circ\text C.\) What is the value of \(t_2 \text{?}\)
1. \(12\)
2. \(14\)
3. \(16\)
4. \(18\)
1. \(12\)
2. \(14\)
3. \(16\)
4. \(18\)
Subtopic: Newton's Law of Cooling |
Level 3: 35%-60%
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