A) \[\frac{43}{3}P\]
B) 8 P
C) 32 P
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 \[P{{V}^{\gamma }}=\] 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 PV^ = constant can be written in terms of other pair of thermodynarnic variables by combining it with the ideal gas law \[(PV=nRT)\]. In doing so, we will find that, \[T{{V}^{\gamma -1}}=\] constant and \[{{T}^{\gamma }}\,{{P}^{1-\gamma }}=\] constant.
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