Question

An ideal gas of volume $V$ and pressure $P$ expands isothermally to volume $16V$ and then compressed adiabatically to volume $V.$ The final pressure of gas is: [$\gamma =1.5$]

• A. $P$
• B. $3P$
• C. $4P$
• D. $6P$

Answer 1

Answer: (C)

$4P$

We know in isothermal condition

$PV=$constant

$PV=P_2\times \left(16V\right)$

$P_2=\frac{P}{16}$

Then, in adiabatic process are have

$P{V}^{\gamma }=const$

$P_2(16V{)}^r=P_3(V{)}^r$

$\frac{P}{16}(16V{)}^{1.5}=P_3(V{)}^{1.5}$

$P_3=\sqrt{16}P$

$P_3=4P$