Question

An ideal gas occupying a volume of $2{dm}^3$ and a pressure of $5bar$ undergoes isothermal and irreversible expansion against external pressure of $1bar$. The final volume of the system and the work involved in the process is :

• A. $10{dm}^{-3},1000J$
• B. $8{dm}^3,-800J$
• C. $10{dm}^3,-810J$
• D. $10m^3,-1000J$

Answer 1

The correct option is C $10{dm}^3,-810J$

$w=-2.303nRTlog\frac{v_2}{v_1}$

$p_1{v}_1=p_2{v}_2$

$\Rightarrow 5\times 2=1\times v_2$

$\Rightarrow v_2=10liters$

$w=-2.303\times 1\times 0.0821\times 300log\frac{10}{2}$

$=-39.6475L$atm

$39.6475\times 101.3$

$4016.30J$

$w=-p\Delta v$

$=-1(10-2)$

$=-8L$ atm

$-8\times 101.3=-810.4J$