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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    The coefficients of thermal conductivities of copper, murcury and glass respectively are\[{{K}_{c}},{{K}_{m}}\] and\[{{K}_{g}}\]such that\[{{K}_{c}}>\text{ }{{K}_{m}}>\text{ }{{K}_{g}}\]. If the same quantity of heat flows per second per unit area of each and corresponding temperature gradients are\[{{X}_{c}},{{X}_{m}}\]and\[{{X}_{g}},\]then

    A) \[{{X}_{c}}=\text{ }{{X}_{m}}=\text{ }{{X}_{g}}\] 

    B)  \[{{X}_{c}}>{{X}_{m}}>\text{ }{{X}_{g}}\]

    C)  \[{{X}_{c}}<{{X}_{m}}<\text{ }{{X}_{g}}\]  

    D)  \[{{X}_{m}}<{{X}_{c}}<\text{ }{{X}_{g}}\]

    Correct Answer: C

    Solution :

     \[\frac{1}{A}=\frac{dQ}{dt}=K\frac{d\theta }{dt}\] \[\therefore \] \[K=\frac{d\theta }{dt}=\]constant \[\Rightarrow \] \[\frac{d\theta }{dt}=\frac{1}{K},\]As\[{{k}_{c}}>{{K}_{m}}>{{K}_{g}}\] Then \[{{\left( \frac{d\theta }{dt} \right)}_{c}}<{{\left( \frac{d\theta }{dt} \right)}_{m}}<{{\left( \frac{d\theta }{dt} \right)}_{g}}\] \[\Rightarrow \] \[{{X}_{c}}>{{X}_{m}}<{{X}_{g}}\]


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