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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion JEE PYQ-Thermometry Calorimetry and Thermal Expansion

  • question_answer
    Ice at \[-20{}^\circ C\] is added to 50 g of water at \[40{}^\circ C\]. When the temperature of the mixture reaches \[0{}^\circ C,\] it is found that 20 g of ice is still un melted. The amount of ice added to the water was close to-            [JEE Main 11-Jan-2019 Morning] (Specific heat of water \[=4.2\text{ }J/g/{}^\circ C\] Specific heat of Ice \[=2.1\text{ }J/g/{}^\circ C\] Heat of fusion of water at \[0{}^\circ C=334\text{ }J/g\])

    A)  60 g   

    B)       50 g

    C)  40 g    

    D)       100 g

    Correct Answer: C

    Solution :

    [c] Let m be the mass of ice added to water.
    \[(m-20)L+mC\Delta {{T}_{1}}=50{{C}_{1}}\Delta {{T}_{2}}\]
    \[\Rightarrow \]\[(m-20)(334)+m\times 2.1(20)=50\times 4.2\times (40)\]
    \[\Rightarrow \]\[m(334+42)=5400+6680\]
    \[\Rightarrow \]\[m=40.1g\]


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