Question

Two samples $\left(A\right)$ and $\left(B\right)$ of gas initially at the same temperature and pressure are compressed from a volume $\left(V\right)$ to a volume $\left(V/2\right)$. One isothermally and the other adiabatically respectively. The final pressure of

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

Answer 1

The correct option is A $A$ is less than that of $B$


$A\to$ isothermal
For isothermal process
$P_1{V}_1=P_2{V}_2$
Or $P_2=\frac{P_1{V}_1}{V_2}$
Or $P_2=P_A=P_1\left(\frac{V}{V/2}\right)=2P_1$
$B\to$ adiabatic
For adiabatic process
$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
Or $P_2=P_B=P_1{\left(\frac{V_1}{V_2}\right)}^{\gamma }=2^{\gamma }{P}_1$
$\because \gamma =1$
So $P_B>P_A$
Hence, option $\left(C\right)$ is correct.