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BHU PMT BHU PMT (Screening) Solved Paper-2007

  • question_answer
    An ideal gas heat engine operates in a Carnot cycle between\[227{}^\circ C\]and\[127{}^\circ C\]. It absorbs 6 kcal at the higher temperature. The amount of heat (in kcal) converted into work is equal to

    A)  1.6                                        

    B)  1.2

    C)  4.8                                        

    D)  3.5

    Correct Answer: B

    Solution :

                     The efficiency of heat engine is\[\eta =1-\frac{{{T}_{2}}}{{{T}_{1}}}\] Or           \[\frac{W}{{{Q}_{1}}}=1-\frac{{{T}_{2}}}{{{T}_{1}}}\] Here,\[{{Q}_{1}}=\]heat absorbed from the source of heat = 6 kcal \[{{T}_{1}}=\]temperature of source \[=227+273=500\text{ }K\] and\[{{T}_{2}}=\] temperature of sink \[=127+273=400\text{ }K\] Hence,    \[\frac{W}{6}=1-\frac{400}{500}\] Or           \[\frac{W}{6}=\frac{100}{500}\]or \[W=1.2\,kcal\] Thus, amount of heat converted into work is \[1.2\,kcal\].


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