BCECE Engineering BCECE Engineering Solved Paper-2003

  • question_answer A gas at NTP is suddenly compressed to one-fourth of its original volume. If \[\gamma \] is supposed to be 3/2, then the final pressure is:

    A)  4 atm                                   

    B)         \[\frac{3}{2}\] atm

    C)         8 atm                                   

    D)         \[\frac{1}{4}\] atm

    Correct Answer: C

    Solution :

    The adiabatic relation between volume and pressure of a gas \[P{{V}^{\gamma }}=\text{constant}\]                 or            \[{{P}_{2}}{{V}_{2}}^{\gamma }={{P}_{1}}{{V}_{1}}^{\gamma }\]                 or            \[{{P}_{2}}={{P}_{1}}{{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma }}\]                      ?(i)                 Given, \[{{P}_{1}}=1atm,\,{{V}_{1}}=V,\,{{V}_{2}}=\frac{V}{4},\gamma =\frac{3}{2}\] Substituting in Eq. (i), we get                 \[{{P}_{2}}=1\times {{\left( \frac{V}{V/4} \right)}^{3/2}}={{(4)}^{3/2}}=8\,\text{atm}\]

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