A) \[\frac{4}{9}%\]
B) \[\frac{2}{3}%\]
C) \[4%\]
D) \[\frac{9}{4}%\]
Correct Answer: A
Solution :
For an adiabatic process, \[p{{V}^{\gamma }}=\]constant (say C) Here \[\gamma =\frac{{{C}_{p}}}{{{C}_{V}}}=\frac{3}{2}\] \[\therefore \] \[p{{V}^{3/2}}=C\] \[\Rightarrow \] \[\log p+\frac{3}{2}\log V=\log C\] \[\Rightarrow \] \[\frac{\Delta \pi }{p}+\frac{3}{2}\frac{\Delta V}{V}=0\] \[\therefore \] \[\frac{\Delta V}{V}=\frac{-2}{3}\frac{\Delta \pi }{p}\] \[\frac{\Delta V}{V}\times 100=\left( \frac{2}{3} \right)\left( \frac{\Delta \pi }{p}\times 100 \right)\] \[=-\frac{2}{3}\times \frac{2}{3}%=-\frac{4}{9}%\] Thus, volume decreases by\[\frac{4}{9}%\].
You need to login to perform this action.
You will be redirected in
3 sec
