A) \[\frac{1}{128}\]
B) 32
C) 128
D) None of these
Correct Answer: C
Solution :
In an adiabatic process \[P{{V}^{\gamma }}=\text{constant}\] Now, \[\text{volume = }\frac{\text{mass}}{\text{density}}\] i.e., \[V=\frac{M}{d}\] \[\therefore \] \[P{{\left[ \frac{M}{d} \right]}^{\gamma }}=\text{constant}\] or \[\frac{P}{{{d}^{\gamma }}}=a,\]new constant. or \[\frac{P}{{{d}^{\gamma }}}=\frac{P}{{{d}^{\gamma }}}\] or \[\frac{P}{P}={{\left( \frac{d}{d} \right)}^{\gamma }}\] but \[\frac{d}{d}=32\]and \[\gamma =\frac{7}{5}\] \[\therefore \] \[\frac{P}{P}={{(32)}^{7/5}}={{\left[ {{(32)}^{1/5}} \right]}^{7}}\] \[={{2}^{7}}\] \[=128\]
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