A hypothetical gas expands adiabatically such that its volume changes from 8 litres to 27 litres. If the ratio of final pressure of the gas to the initial pressure of the gas is , then the ratio will be [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A hypothetical gas expands adiabatically such that its volume changes from 8 litres to 27 litres. If the ratio of final pressure of the gas to the initial pressure of the gas is $\frac{16}{81}$ , then the ratio $\frac{C_{P}}{C_{V}}$ will be [2023]

1 $\frac{4}{3}$

2 $\frac{3}{1}$

3 $\frac{1}{2}$

4 $\frac{3}{2}$

Ans.
(1)

$Let γ be the ratio of \frac{C_{p}}{C_{v}}$

$Then for adiabatic process$

$P V^{γ} = constant$

$\frac{P_{i}}{P_{f}} = {(\frac{V_{f}}{V_{i}})}^{γ}$

$\frac{81}{16} = {(\frac{27}{8})}^{γ}$

$γ = \frac{4}{3}$

Want Us to Email you About Special Offers & Updates?