RAJASTHAN PMT Rajasthan - PMT Solved Paper-2003

  • question_answer
    The fractional change in internal energy when a gas is cooled from \[927{}^\circ C\] to \[27{}^\circ C\] is

    A)  0.25                                      

    B)  0.75

    C)  1                            

    D)         0.67

    Correct Answer: B

    Solution :

    Initial internal energy, \[{{U}_{1}}=n{{C}_{\upsilon }}{{T}_{1}}\] Final internal energy, \[{{U}_{2}}=n\,{{C}_{v}}{{T}_{2}}\] \[\therefore \]Fractional change                                 \[=\frac{{{U}_{1}}-{{U}_{2}}}{{{U}_{1}}}=\frac{n{{C}_{\upsilon }}({{T}_{1}}-{{T}_{2}})}{_{n}{{C}_{\upsilon }}{{T}_{1}}}\]                                 \[=1-\frac{{{T}_{2}}}{{{T}_{1}}}=1-\frac{273+27}{273+927}\]                                 \[=1-\frac{300}{1200}\]                                 \[=1-\frac{1}{4}=\frac{3}{4}=0.75\]


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