Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2011PhysicsThermal Properties of MatterActual

A copper sphere cools from 62^ C to 50^ C in 10 minutes and to 42^ C in the next 10 minutes. Calculate the temperature of the surroundings.

Options

  1. A18.01^ C
  2. B26^ C
  3. C10.6^ C
  4. D20^ C

Correct answer

B. 26^ C

Step-by-step solution

By Newton's law of cooling, ₁- ₂ t =-k [ ₁+ ₂ 2 - ₀ ] ....(1) A sphere cools from 62^ C to 50^ C in 10 ~min . 62-50 10 =- k [ 62+50 2 - ₀ ] ....(2) Now, sphere cools from 50^ C to 42^ C in next 10 ~min . 50-42 10 =- k [ 50+42 2 - ₀ ] ....(3) Dividing eq ^ n . (2) by (3) we get, 56- ₀ 46- ₀ = 1.2 0.8 or 0.4 ₀=10.4 Hence ₀=26^ C

Practice Thermal Properties of Matter on Quantrex Academy →

More from Thermal Properties of Matter

A solid metallic cube having total surface area 24 ~m ^2 is uniformly heated. If its temperature is increased by 10^ C , calculate the increase in volume of the cube. ( . Given : . 2024A bowl filled with very hot soup cools from 98^ C to 86^ C in 2 minutes when the room temperature is 22^ C . How long it will take to cool from 75^ C to 69^ C ? 2023The two ends of a rod of length L and a uniform crosssectional area A are kept at two temperatures T₁ and T ₂ ( ~T ₁> T ₂ ) . The rate of heat transfer, dQ dt through the rod in a 2021A crystal has a coefficient of expansion 13 10⁻⁷ in one direction and 231 10⁻⁷ in every direction at right angles to it. Then the cubical coefficient of expansion is 2020Steam at 100 ° C is passed into 1 . 1 kg of water contained in a calorimoter of water equivalent to 0 . 2 kg at 15 ° C till the temperature of the calorimeter and its con 2018Three rods of identical cross-sectional area and made from the same metal, form the sides of an isosceles triangle A B C right angled at B as shown in figure. The point A and B are 2018If temperature of a black body increases from 300 K to 900 K , then the rate of energy radiation increases by 2017Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the l 2016 Full Thermal Properties of Matter list All BITSAT PYQs