JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Question Bank Self Evaluation Test - Thermal Properties of Matter

  • question_answer
    A mass of 50g of water in a closed vessel, with surroundings at a constant temperature takes 2 minutes to cool from \[30{}^\circ C\] to\[25{}^\circ C\]. A mass of 100g of another liquid in an identical vessel with identical surroundings takes the same time to cool from \[30{}^\circ C\] to \[25{}^\circ C\]. The specific heat of the liquid is: (The water equivalent of the vessel is 30g.)   

    A) 2.0 kcal/kg

    B) 7 kcal/kg

    C) 3 kcal/kg

    D) 0.5 kcal/kg

    Correct Answer: D

    Solution :

    [d] \[\frac{\left( {{m}_{w}}{{C}_{m}}+W \right)\Delta T}{t}=\frac{\left( {{m}_{\ell }}{{C}_{\ell }}+W \right)\Delta T}{t}\] (W=water equivalent of the vessel) or \[{{m}_{w}}{{C}_{w}}={{m}_{\ell }}{{C}_{\ell }}\] \[\therefore \] Specific heat of liquid, \[C=\frac{{{m}_{w}}{{C}_{w}}}{{{m}_{\ell }}}\] \[=\frac{50\times 1}{100}=0.5kcal/kg\]


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