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DUMET Medical DUMET Medical Solved Paper-2006

  • question_answer
    Six moles of \[{{O}_{2}}\] gas is heated from \[{{20}^{o}}C\] to \[{{35}^{o}}C\] at constant volume. If specific heat capacity l constant pressure is 8cal/mol-K and R = 8.31 J/mol-K, what is change in internal energy of gas?

    A)  180 cal        

    B)  300 cal         

    C)  360 cal         

    D)  540 cal         

    Correct Answer: D

    Solution :

     Consider \[n\] moles of a gas which undergo isochoric process, i.e., V = constant. From first law of thermodynamics, \[\Delta Q=\Delta W+\Delta U\] ... (i) Here, \[\Delta W=0\] as V = constant \[\Delta Q=n{{C}_{V}}\Delta T\] Substituting in Eq. (i), we get \[\Delta U=n{{C}_{V}}\Delta T\] ... (ii) Mayors formula can be written as \[{{C}_{P}}-{{C}_{V}}=R\] \[\Rightarrow \] \[{{C}_{V}}={{C}_{P}}-R\] ... (ii) From Eqs. (ii) and (iii), we have \[\Delta U=n({{C}_{P}}-R)\Delta T\] Given, \[n=6,\,{{C}_{P}}=8\,cal/mol-K\], \[R=8.31\,J/mol-K\] \[\approx 2\,cal/mol-K\] Hence, \[\Delta U=6(8-2)\,(35-20)\] \[=6\times 6\times 15\] = 540 cal


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