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JEE Main & Advanced JEE Main Paper (Held On 10-Jan-2019 Evening)

  • question_answer
    An ideal gas undergoes isothermal compression from \[5{{m}^{3}}\] to \[1\text{ }{{m}^{3}}\] against a constant external pressure of \[4\text{ }N{{m}^{-}}^{2}\]. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J \[mo{{l}^{-1}}\text{ }{{K}^{-1}}\], the temperature of Al increases by: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

    A) \[\frac{2}{3}\]K                                    

    B) \[\frac{3}{2}\]K   

    C) 1 K                  

    D)                  2 K

    Correct Answer: A

    Solution :

    \[w=-\int{{{P}_{ext}}dV}\] \[=-\,4\left( 1-5 \right)=16\text{ }J\] \[\Delta U=0\] for isothermal process (ideal gas) \[\therefore \,\,\,\,q=-w\] \[\therefore \,\,\,q=-16\,J\And \,\,\left| q \right|=nCv\Delta T\] \[\left| -16 \right|=1\times 24\times \Delta T\] \[\therefore \,\,\Delta T=\frac{2}{3}K\]


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