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

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

$T_1V_1^{\gamma -1}$=$T_2V_2^{\gamma -1}$

$273\times \left ( \frac{1}{0.5}\right )^\left ( {\gamma -1}\right )$=$T_2$

$T_2$=273$\times \left ( 2\right )^\left ( 0.3\right )$

$T_2$=336.1k

Now the is cooled at constant pressure i.e.

$\frac{V_2}{T_2}$=$\frac{V_3}{T_3}$

$\frac{0.5}{336.1}$=$\frac{V_3}{273}$

$\frac{0.5}{336.1}$=$\frac{V_3}{273}$

$V_3$=0.406 L