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MHT CET20228 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

Water at 100^ C cools in 10 minutes to 80^ C in a room temperature of 25^ C , then the temperature of water after 20 minutes will be

Options

  1. A65.33^ C
  2. B69.33^ C
  3. C60.33^ C
  4. D63.33^ C

Correct answer

A. 65.33^ C

Step-by-step solution

aligned & d T ~d t =-k(T-25) & T-25=e^ -k t+c & T=25+e^c e^ -k t & for t=0, T=100 & e^c=75 & T=25+75 e^ -k t & for t=10, T=80 & 80=25+75 e^ -k 10 & -10 k= ( 11 55 ) & i.e., T=25+75 e^ ( 1 10 11 15 ) t & Now for t=20, T=25+75 e^ 20 1 10 11 15 =25+75 ( 11 15 )^2 & T=25+40.33=65.33 & aligned

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