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JEE Main201911 Jan 2019Evening ShiftPhysicsKinetic Theory of GasesActual

A metal ball of mass 0.1 ~kg is heated upto 500^ C and dropped into a vessel of heat capacity 800 JK ⁻¹ and containing 0.5 ~kg water. The initial temperature of water and vessel is 30^ C . What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg ⁻ ¹ ~K ⁻¹ and 400 Jkg ⁻¹ ~K ⁻¹ ]

Options

  1. A15 %
  2. B30 %
  3. C25 %
  4. D20 %

Correct answer

D. 20 %

Step-by-step solution

Assume final temperature = T ^ C Heat lass = Heat gain = ms T m _ B s _ B T _ B = m _ w s _ w T _ w 0.1 400 (500- T ) =0.5 4200 ( T -30)+800( ~T -30) 40(500- T )=( T -30)(2100+800) 20000-40 ~T =2900 ~T -30 2900 20000+30 2900= T (2940) T =30.4^ C T T 100= 6.4 30 100=21 % so the closest answer is 20 % .

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