Question

Two samples $A$ and $B$ of a gas, initially at the same pressure and temperature, are compressed from volume $V$ to $V/2$ ($A$ 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

Answer: (C)

For sample $A\to$ in isothermal process By Boyle's law
$p_1{V}_1=p_2{V}_2$
$\Rightarrow p_2=p\left(\frac{V_1}{V_2}\right)$
$p_2=p\left(\frac{V}{V/2}\right)=2p$
For sample $B\to$ in adiabatic process By Poisson's law $p{V}_1^{\gamma }=p_2{V}_2^{\gamma }$
$\therefore p_2=p(2{)}^{\gamma }$
$\because \gamma >1$
$\therefore 2\gamma >2$
$\therefore 2\gamma p>2p$
or ${\left(p_2\right)}_B>{\left(p_2\right)}_A$
Final pressure of $A$ is less than pressure of $B$.