A) 8 times
B) 16 times
C) 32 times
D) 128 times
Correct Answer: C
Solution :
In an adiabatic process \[P{{V}^{\gamma }}=\text{constant}\] (\[\gamma \]for monoatomic gas is \[\frac{5}{3}\]) Hence, \[{{P}_{1}}V_{1}^{\gamma }={{P}_{2}}V_{2}^{\gamma }\] \[\Rightarrow \] \[\frac{{{P}_{2}}}{{{P}_{1}}}={{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma }}={{\left( \frac{{{V}_{1}}}{\frac{1}{8}{{V}_{1}}} \right)}^{\gamma }}\] Given: \[{{V}_{2}}=\frac{1}{8}{{V}_{1}}\] \[={{\left( \frac{8}{1} \right)}^{5/3}}={{[{{(2)}^{3}}]}^{5/3}}={{(2)}^{5}}=32\] The final pressure will be 32 times of original pressure.
You need to login to perform this action.
You will be redirected in
3 sec
