Answer:
[tex]W=P_1V_1\ ln\dfrac{V_2}{V_1}[/tex]
Explanation:
Lets take
At initial position
[tex]Pressure = P_1[/tex]
[tex]Volume = V_1[/tex]
At final position
[tex]Pressure = P_2[/tex]
[tex]Volume = V_2[/tex]
SI unit
[tex]Pressure =N/m^2[/tex]
[tex]Volume =m^3[/tex]
English units
[tex]Pressure =lb/in^2[/tex]
[tex]Volume =in^3[/tex]
For expansion process:
As we know that work done given as
[tex]W=\int P.dV[/tex]
We know that for isothermal process
P.V = C
[tex]P_1V_1=P_2V_2=C[/tex]
[tex]W=\int_{V_1}^{V_2}\dfrac{P_1V_1}{V}.dV[/tex]
[tex]W=P_1V_1\ ln\dfrac{V_2}{V_1}[/tex]
Expression for expansion and for compression will be same.
