A) 4 R
B) 2.5 R
C) 3R
D) \[4\frac{R}{3}\]
Correct Answer: C
Solution :
\[p=k{{\forall }^{-1}}=k\] Comparision with a polytropic process \[\left( p{{\forall }^{n}}=\text{constant} \right),\,\text{gives}\,\text{n}=-1\] \[W=\frac{{{p}_{1}}{{\forall }_{1}}-{{p}_{2}}{{\forall }_{2}}}{n-1}=\frac{\mu R{{T}_{1}}-\mu R{{T}_{2}}}{-1-1}\] \[\therefore \] \[W=\frac{\mu R({{T}_{1}}-{{T}_{2}})}{-2}=\frac{-\mu R\Delta \Tau }{-2}=\frac{\mu R\Delta \Tau }{2}\] Also, \[\Delta Q=\Delta U+\Delta W\] \[\therefore \] \[\mu C\Delta \Tau =\mu {{C}_{V}}\Delta T+\frac{\mu R\Delta \Tau }{2}\] or, \[C={{C}_{v}}+\frac{R}{2}=\frac{5}{2}R+\frac{R}{2}=3R\] Hence, the correction option is [c].
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