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KVPY Sample Paper KVPY Stream-SX Model Paper-10

  • question_answer
    A gas present in a cylinder fitted with a frictionless piston expands against a constant pressure of 1 atm from a volume of 2 litre to a volume of 6 litre. In doing so, it absorbs \[800\text{ }\operatorname{J}\]heat from surroundings. Determine increase in internal energy of process.

    A) 385 J               

    B) 395 J

    C) 380 J               

    D) 378 J

    Correct Answer: B

    Solution :

    Since, work is done against constant pressure and thus, irreversible.
    Given, \[\Delta \operatorname{V}=\left( 6-2 \right)=4\operatorname{litre},P=1atm\]
    \[\therefore \operatorname{W}=-1\times 4\]litre-atm\[=-\frac{1\times 4\times 1.987}{0.0821}\operatorname{cal}\]
    \[\left( since 0.0821 litre-atm=1.987cal \right)\]
    \[=-96.21cal=-096.81\times 4.184J\]
    \[\left( \because 1\operatorname{cal}=4.184J \right)\]
    \[=-405.05\operatorname{J}\]
    Now from first law of thermodynamics
    \[\operatorname{q}=\Delta \operatorname{U}-W\]
    \[800=\Delta U+405.05\]
    \[\therefore \Delta U=394.95J\approx 395J\]


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