Question

Two litres of $N_2$ at $0^C$ and $5atm$ pressure are expanded isothermally against a constant external pressure of $1atm$ until the pressure of gas reaches $1atm$.

Assuming gas to be ideal, work of expansion is:

• A. $810J$
• B. $-810J$
• C. $81J$
• D. None of these

Answer 1

Answer: (B)

$-810J$

Since the external pressure is greatly different from the pressure of

$N_2$ and thus, the process is irreversible.

$w=-P_{ext}(V_2-V_1)$

$w=-1\times (V_2-V_1)$

Given $V_1=2$ litre $V_2=?$ $T=273K$

$P_1=5atm$ $P_2=1atm$

$\therefore P_1{V}_1=P_2{V}_2$

$\therefore V_2=\frac{2\times 5}{1}=10$ litre

$\therefore w=-1\times (10-2)=-8$ litre atm

$\therefore =-\frac{8\times 1.987}{0.0821}calorie=-\frac{8\times 1.987\times 4.184}{0.0821}J=-810.10$ joule