A container with $1 \,kg$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700\, Wm ^{-2}$ and it is absorbed by the water over an effective area of $0.05\, m ^{2}$ .Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${ }^{\circ} C$ ) in the temperature of water and the surroundings after a long time will be _______ .(Ignore effect of the container, and take constant for Newton's law of cooling $=0.001\, s ^{-1}$, Heat capacity of water $=4200\, J \,kg ^{-1} K ^{-1}$ )
Correct Answer: 8.32 - 8.34
Solution and Explanation
\(Δ T = 8.33\)
Top Questions on Heat Transfer
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Three conductors of same length having thermal conductivity \(k_1\), \(k_2\), and \(k_3\) are connected as shown in figure. Area of cross sections of 1st and 2nd conductor are same and for 3rd conductor it is double of the 1st conductor. The temperatures are given in the figure. In steady state condition, the value of θ is ________ °C. (Given: \(k_1\) = 60 Js⁻¹m⁻¹K⁻¹,\(k_2\) = 120 Js⁻¹m⁻¹K⁻¹, \(k_3\) = 135 Js⁻¹m⁻¹K⁻¹)
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Questions Asked in JEE Advanced exam
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity):
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(Here, the inverse trigonometric function $ \tan^{-1} x $ assumes values in $ \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) $.)- JEE Advanced - 2025
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Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
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