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JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Sample Paper Topic Test - Thermometry, Calorimetry & Thermal Expansion

  • question_answer
    Four cubes of ice at \[-10{}^\circ C\] each one gm is taken out from the refrigerator and are put in 150 gm of water at \[20{}^\circ C\]. The temperature of water when thermal equilibrium is attained. Assume that no heat is lost to the outside and water equivalent of container is 46 gm. (Specific heat capacity of water \[=\text{ }1\text{ }cal/gm-{}^\circ C\], Specific heat capacity of ice \[=\text{ }0.5\text{ }cal/gm-{}^\circ C\], Latent heat of fusion of ice \[=\text{ }80\text{ }cal/gm)\]

    A) \[0{}^\circ C\]                         

    B) \[-10{}^\circ C\]

    C) \[17.9{}^\circ C\]    

    D) None

    Correct Answer: C

    Solution :

                
    Heat gained by ice = Heat lost by water + Heat lost by container
    Initial Temperature of container = \[20{}^\circ \]
    \[4\times \frac{1}{2}\times 10+4\times 80+4\times 1\times (T-0)\]
    \[=196\times 1\times (20-T)\]
    \[20+320+4T=196\times 20-196\,\,T\]  
    \[200\,T\,=\,196\,\times \,20\,-\,340\]
    \[T=\frac{3580}{200}=17.9{}^\circ C\]


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