A) 0.76 : 1
B) 1 : 1
C) 0.66 : 1
D) 0.86 : 1
Correct Answer: A
Solution :
We are given that an ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically. So we have for an adiabatic process \[{{p}_{f}}V_{f}^{\gamma }={{p}_{i}}V_{i}^{\gamma }\] Here, \[{{p}_{i}}=2p,\,\,{{V}_{i}}=\frac{V}{2},{{V}_{f}}=V\] So, \[\frac{{{p}_{f}}}{{{p}_{i}}}=2{{\left( \frac{V}{2V} \right)}^{\gamma }}=2\times {{2}^{-\gamma }}=2\times {{2}^{-1.4}}\] \[=2\times 0.38=0.76\]
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