Question

Two samples of an ideal gas are initially at the same temperature and pressure. They are each compressed reversibly from a volume V to volume V/2, one isothermally (sample 1), the other adiabatically (sample 2). Part A In which sample is the final pressure greater?

Answer 1

Answer:In adiabatic case

Explanation:

Let us suppose Initial condition

$P_1,V$

be the initial pressure and volume of gas

and $P_2,\frac{V}{2}$

be the final pressure

$\left ( a\right )$In Isothermal case

Temprature is costant therefore

PV=constant

$P_1V=P_2\frac{V}{2}$

$P_2=2P_1$

for adiabatic case

$PV^{\gamma }=constant$

$P_1V^{\gamma }=P_2\left (\frac{V}{2}\right )^{\gamma }$

$P_2=2^{\gamma }P_1$

and we know$\gamma$ is greater than 1

therefore In adiabatic case pressure will be high.