ThermodynamicsHard

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 $\left( \frac{q_{\text{path-I}}}{q_{\text{path-II}}} \right)$is

Options

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

Solution

For both paths, ΔU = 0, as ΔT = 0.

$\frac{q_{\text{path-I}}}{q_{\text{path-II}}} = \frac{- w_{\text{path-I}}}{- w_{\text{path-II}}} = \frac{PV.\ln\frac{V_{2}}{V_{1}}}{(P.\Delta V)_{1} + (P.\Delta V)_{2}} = \frac{10 \times 1 \times \ln\left( \frac{10}{1} \right)}{5(2 - 1) + 1(10 - 2)} = \frac{10 \times 2.303}{13}$

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