JEE Main & Advanced Sample Paper JEE Main - Mock Test - 1

  • question_answer
    A calorimeter of negligible heat capacity contains \[100\text{ }c{{m}^{3}}\] of water at\[40{}^\circ C\]. The water cools to \[35{}^\circ C\] in 5 minutes. The water is now replaced by oil of equal volume at\[40{}^\circ C\]. Find the time taken for the temperature to become \[35{}^\circ C\] under similar conditions Specific heat capacities of water and oil are \[4200\frac{J}{kg-K}\] and \[2100\frac{J}{kg-K}\] respectively. Density of oil is \[800\,\,kg/{{m}^{3}}.\]

    A) 10 min  

    B) 2 min          

    C) 20 min               

    D) 8 min

    Correct Answer: B

    Solution :

    [b] \[\frac{-({{T}_{2}}-{{T}_{1}})}{\Delta {{t}_{1}}}=\frac{k'}{{{m}_{1}}{{s}_{1}}}\left[ \frac{{{T}_{1}}+{{T}_{2}}}{2}-{{T}_{s}} \right]\] \[\frac{-({{T}_{2}}-{{T}_{1}})}{\Delta {{t}_{2}}}=\frac{k'}{{{m}_{2}}{{s}_{2}}}\left[ \frac{{{T}_{1}}+{{T}_{2}}}{2}-{{T}_{s}} \right]\] \[\frac{\Delta {{t}_{2}}}{\Delta {{t}_{1}}}=\frac{{{m}_{2}}{{s}_{2}}}{{{m}_{1}}{{s}_{1}}}\] \[\frac{\Delta {{t}_{2}}}{5}=\left( \frac{800}{1000} \right)\times \left( \frac{1}{2} \right)=\frac{1}{2.5}\]  \[\Delta {{t}_{2}}=2\] minute    


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