Question

Suppose 1.00 L of a gas with \gamma γ = 1.30, initially at 273 K and 1.00 atm, is suddenly compressed adiabatically to half its initial volume. If the gas is then cooled to 273 K at constant pressure, what is its final volume in L?

Answer 1

Answer:0.4061 L

Step-by-step explanation:

let initial volume of gas be
`V_1`=1 L

`\gamma` =1.3

initial temprature
`\left ( T_1\right )`=273k

Now if gas is compressed adiabatically to half of its initial volume then

`V_2`=0.5L

Using adiabatic relation

`TV^(\gamma -1)`=constant

`T_1V_1^(\gamma -1)`=
`T_2V_2^(\gamma -1)`

`273* \left ( (1)/(0.5)\right )^\left ( {\gamma -1}\right )`=
`T_2`

`T_2`=273
`* \left ( 2\right )^\left ( 0.3\right )`

`T_2`=336.1k

Now the is cooled at constant pressure i.e.

`(V_2)/(T_2)`=
`(V_3)/(T_3)`

`(0.5)/(336.1)`=
`(V_3)/(273)`

`(0.5)/(336.1)`=
`(V_3)/(273)`

`V_3`=0.406 L