Answer:
The value is [tex]W = - 17.53 \ J[/tex]
Explanation:
From the question we are told that
The volume is [tex]V = 0.230 \ L = 0.230 *10^{-3} \ m^{-3}[/tex]
The initial pressure is [tex]P_1 = 1.01105 \ Pa[/tex]
The initial temperature is [tex]T_1 = 3.00*10^2 \ K[/tex]
The final temperature is [tex]T_2 = 489 \ K[/tex]
Generally for an adiabatic process the workdone is mathematically represented as
[tex]W = - \Delta U[/tex]
Here [tex]\Delta U[/tex] is the internal energy of the system which is mathematically represented as
[tex]\Delta U = \frac{3}{2} * nR \Delta T[/tex]
So
[tex]W = - \frac{3}{2} * nR \Delta T[/tex]
Generally from ideal gas equation we have that
[tex]n = \frac{P_1V }{ RT_1 }[/tex]
Here R is the gas constant with value [tex]R = 8.314 J/mol\cdot K[/tex]
So
[tex]n = \frac{1.01 *0^{5} * 0.230 *10^{-3}}{ 8.314 * 3.0*10^2 }[/tex]
=> [tex]n = 0.009313 \ mol[/tex]
So
[tex]W = - \frac{3}{2} * 0.009313 * 8.314 * (451 - 3.00*10^2)[/tex]
=> [tex]W = - 17.53 \ J[/tex]
