A) \[\frac{a}{b}\]
B) \[\frac{b+1}{b}\]
C) \[\frac{a+1}{a}\]
D) \[\frac{b}{a}\]
Correct Answer: B
Solution :
[b] For an adiabatic process \[dQ=0\] \[d\,U+d\,W=0\] \[d\,[a+bpV]+Pd\,V=0\] \[0+b\,Pd\,V+bVd\,P+Pd\,V=0\] \[(b+1)\text{ }Pd\,V+bVd\,P=0\] \[(b+1)\text{ }Pd\,V+bVd\,P=0\] \[(b+1)\frac{dV}{V}=-\frac{bdP}{P}\] Integrates both \[(b+1)\int{V+b}\int{P=\,const}\] \[\int{{{V}^{b+1}}{{P}^{b}}=\,const}\,\] Compare with \[P{{V}^{\gamma }}=K\] \[Y=\frac{b+1}{b}\]
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