Question

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

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

Answer 1

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

For path-I

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

$=-nRT\times 2.303$

$q_1=-W=nRT\times 2.303$

For Path-II

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

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

$=-1.3RT.n$

$\therefore q_{II}=1.3nRT$

​

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

Hence, the correct option is $\text{A}$