MCQ
The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from $5$ litres to $4$ litres. The ratio of initial pressure to final pressure is:
- A$\frac{4}{5}$
- B$\frac{16}{25}$
- ✓$\frac{8}{5 \sqrt{5}}$
- D$\frac{2}{\sqrt{5}}$
✓
Answer
Correct option: C.
$\frac{8}{5 \sqrt{5}}$
c
For Adiabatic process
For Adiabatic process
$P_i V_i=P_f V_f^\gamma$
$P_i(5)^{1.5}=P_f(4)^{1.5}$
$\frac{P_i}{P_f}=\left(\frac{4}{5}\right)^{\frac{3}{2}}=\frac{4}{5} \cdot\left(\frac{4}{5}\right)^{\frac{1}{2}} \Rightarrow \frac{8}{5 \sqrt{5}}$
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