OnlineCBT
Chemistry · THERMODYNAMICS
हिन्दीOne mole of an ideal gas at \( 300\text{ K} \) is expanded isothermally and reversibly from an initial volume \( V_1 \) to a final volume \( V_2 \) such that \( w = -5.74\text{ kJ} \). If the same gas is expanded irreversibly against a constant external pressure of \( 1\text{ bar} \) between the same initial and final volumes, where \( V_1 = 2.48\text{ L} \), what is the value of \( w_{\text{irrev}} \)? (Take \( R = 8.314\text{ J}\cdot\text{K}^{-1}\cdot\text{mol}^{-1} \), \( \ln 10 = 2.303 \), \( 1\text{ L}\cdot\text{bar} = 100\text{ J} \))
Correct answer · Option 3
\( -2232\text{ J} \)
Explanation
\( w_{\text{rev}} = -2.303 nRT \log(V_2/V_1) \implies -5740 = -2.303 \times 1 \times 8.314 \times 300 \log(V_2/V_1) = -5740 \log(V_2/V_1) \implies V_2/V_1 = 10 \). Thus \( V_2 = 10 \times 2.48 = 24.8\text{ L} \). \( w_{\text{irrev}} = -p_{\text{ex}}(V_2 - V_1) = -1\text{ bar} \times (24.8 - 2.48)\text{ L} = -22.32\text{ L}\cdot\text{bar} = -2232\text{ J} \).
