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

Step-by-step explanation:

Let us suppose Initial condition

`P_1,V`

be the initial pressure and volume of gas

and
`P_2,(V)/(2)`

be the final pressure

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

Temprature is costant therefore

PV=constant

`P_1V=P_2(V)/(2)`

`P_2=2P_1`

for adiabatic case

`PV^(\gamma )=constant`

`P_1V^(\gamma )=P_2\left ((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.