Question

Two samples $A$ and $B$ of a gas initially at the same pressure and temperature are compressed from volume $V$ to $\frac{V}{2}$ ($A$ isothermally and $B$ adiabatically). The final pressure of $A$ is

• A. greater than the final pressure of $B$
• B. equal to the final pressure of $B$
• C. less than the final pressure of $B$
• D. twice the final pressure of $B$

Answer 1

The correct option is C less than the final pressure of $B$

For isothermal process, $PV=$ constant

$P_1{V}_1=P_2{V}_2$

$⟹P_2=2P_1$

For adiabatic process, $P{V}^{\gamma }$ = constant

$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$

$⟹P_2=P_1(\frac{V_1}{V_2}{)}^{\gamma }$

$⟹P_2=P_1{2}^{\gamma }$

Since, $\gamma$ is always greater than 1, For the same change in volume, there will be a greater change in pressure for adiabatic process than that for isothemral process.