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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?

1 Answer

1 vote

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

User Bojian Zheng
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