A) \[\frac{43}{3}P\]
B) \[8P\]
C) \[32P\]
D) \[\frac{24}{5}P\]
Correct Answer: C
Solution :
The condition that must be obeyed by an ideal gas in an adiabatic process is given by \[P{{V}^{\gamma }}=\text{constant}\] or \[{{P}_{1}}{{V}_{1}}^{\gamma }={{p}_{2}}{{V}_{2}}^{\gamma }\] or \[{{P}_{2}}={{P}_{1}}{{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma }}\] Here, \[{{P}_{1}}=P,\frac{{{V}_{2}}}{{{V}_{1}}}=\frac{1}{8},\gamma =\frac{5}{3}\] \[\therefore \] \[{{P}_{2}}=P{{(8)}^{5/3}}\] or \[{{P}_{2}}=P{{({{2}^{3}})}^{5/3}}=32\,P\] Note: The equation \[P{{V}^{\gamma }}=\]constant can be written in terms of other pair of thermodynamic variables by combining it with the ideal gas law\[(PV=nRT).\]In doing so, we will find that, \[T{{V}^{\gamma -1}}=\]constant and \[{{T}^{\gamma }}{{P}^{1-\gamma }}=\text{constant}\text{.}\]
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