Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Physics
Chapter
Thermal Properties of Matter

BITSAT 2011 · Physics · Thermal Properties of Matter

A copper sphere cools from 62^ ^ C to 50^ ^ C in 10 minutes and to...

A copper sphere cools from 62∘C62^{{}^{\circ}} \mathrm{C} to 50∘C50^{{}^{\circ}} \mathrm{C} in 10 minutes and to 42∘C42^{{}^{\circ}} \mathrm{C} in the next 10 minutes. Calculate the temperature of the surroundings.

Options

  1. A18.01∘C18.01^{{}^{\circ}} \mathrm{C}
  2. B26∘C26^{{}^{\circ}} \mathrm{C}
  3. C10.6∘C10.6^{{}^{\circ}} \mathrm{C}
  4. D20∘C20^{{}^{\circ}} \mathrm{C}

Correct answer

B. 26∘C26^{{}^{\circ}} \mathrm{C}

Step-by-step solution

By Newton's law of cooling, θ1−θ2t=−k[θ1+θ22−θ0]....(1)Aspherecoolsfrom62∘Cto50∘Cin10min.62−5010=−k[62+502−θ0]....(2)Now,spherecoolsfrom50∘Cto42∘Cinnext10min.50−4210=−k[50+422−θ0]....(3)Dividingeqn \frac{\theta_{1}-\theta_{2}}{t}=-k \left[\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0}\right]....(1) A sphere cools from 62^{{}^{\circ}} \mathrm{C} to 50^{{}^{\circ}} \mathrm{C} in 10 \mathrm{ min}. \frac{62-50}{10}=-\mathrm{k} \left[\frac{62+50}{2}-\theta_{0}\right]....(2) Now, sphere cools from 50^{{}^{\circ}} \mathrm{C} to 42^{{}^{\circ}} \mathrm{C} in next 10 \mathrm{ min}.\frac{50-42}{10}=-\mathrm{k}\left[\frac{50+42}{2}-\theta_{0}\right]....(3) Dividing eq ^{\text{n }}.(2)by(3)weget,56−θ046−θ0=1.20.8or0.4θ0=10.4. (2) by (3) we get, \frac{56-\theta_{0}}{46-\theta_{0}}=\frac{1.2}{0.8} or 0.4 \theta_{0}=10.4 Hence \theta_{0}=26^{{}^{\circ}} C\mathrm{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… BITSAT 2024A bowl filled with very hot soup cools from 98^ ^ ∘ C to 86^ ^ ∘ C in 2 minutes when the… BITSAT 2023The two ends of a rod of length L and a uniform crosssectional area A are kept at two… BITSAT 2021A crystal has a coefficient of expansion 13 × 10^ -7 in one direction and 231 × 10^ -7 in… BITSAT 2020Steam at 100 ° C is passed into 1. 1kg of water contained in a calorimoter of water… BITSAT 2018Three rods of identical cross-sectional area and made from the same metal, form the sides… BITSAT 2018If temperature of a black body increases from 300K to 900K , then the rate of energy… BITSAT 2017Two spheres of different materials one with double the radius and one-fourth wall… BITSAT 2016 Full Thermal Properties of Matter list All BITSAT PYQs