Question

An ideal gas undergoes isothermal expansion from ($10atm$, $1L$) to ($1atm$, $10L$) either by path-I (infinite stage expansion) or by path II (first against $5atm$ and then against $1atm$). The value of $\left(\frac{q_{path-I}}{q_{path-II}}\right)$ is

• A. $\frac{2.303}{1.3}$
• B. $\frac{1.3}{2.303}$
• C. $\frac{1.0}{13\times 2.30}$
• D. $13\times 2.303$

Answer 1

The correct option is A $\frac{2.303}{1.3}$

For path-I

$W=-nRTIn\frac{V_2}{V_1}=-nRTIn\left(\frac{10}{1}\right)$

$=-nRT\times 2.303$

$q_1=-W=nRT\times 2.303$

For Path-II

$W=-5atm(\frac{nRT}{P_2}-\frac{nRT}{P_1})-1atm(\frac{nRT}{P_2^1}-\frac{nRT}{P_1^1})$

$=-nRT\{(\frac{5}{P_2}-\frac{5}{P_1})+(\frac{1}{P_2^1}-\frac{1}{P_1^1})\}$

$=-1.3RT.n$

$\therefore q_{II}=1.3nRT$

$\therefore \frac{q_I}{q_{II}}=\frac{2.303}{1.3}$