Question:
एक आदर्श गैस के दो मोल \(300K\) पर \(10L\) से \(100L\) तक मुक्त प्रसार (free expansion) करते हैं। \(\Delta S_{system}\) और \(\Delta S_{surroundings}\) का मान है :
एक आदर्श गैस के दो मोल \(300K\) पर \(10L\) से \(100L\) तक मुक्त प्रसार (free expansion) करते हैं। \(\Delta S_{system}\) और \(\Delta S_{surroundings}\) का मान है :
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Free expansion irreversible process है, लेकिन ideal gas के लिए \(\Delta U=0\) होता है।
Updated On: Jun 22, 2026
- \(\Delta S_{system}=0;\;\Delta S_{surroundings}=4.606R\)
- \(\Delta S_{system}=4.606R;\;\Delta S_{surroundings}=0\)
- \(\Delta S_{system}=0;\;\Delta S_{surroundings}=0\)
- \(\Delta S_{system}=4.606R;\;\Delta S_{surroundings}=-4.606R\)
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The Correct Option is B
Solution and Explanation
पद 1: प्रश्न को समझना
यह free expansion है।
पद 2: मुख्य सूत्र या दृष्टिकोण
Free expansion में: \[ q=0,\;w=0 \] For ideal gas: \[ \Delta U=0 \] Entropy change: \[ \Delta S=nR\ln\frac{V_2}{V_1} \] पद 3: विस्तृत व्याख्या
Given: \[ n=2 \] \[ V_1=10L,\;V_2=100L \] So: \[ \Delta S=2R\ln\frac{100}{10} \] \[ =2R\ln10 \] \[ =2R(2.303) \] \[ =4.606R \] Surroundings: \[ \Delta S_{surroundings}=0 \] because no heat exchange.
पद 4: अंतिम उत्तर
अतः सही विकल्प (B) है।
यह free expansion है।
पद 2: मुख्य सूत्र या दृष्टिकोण
Free expansion में: \[ q=0,\;w=0 \] For ideal gas: \[ \Delta U=0 \] Entropy change: \[ \Delta S=nR\ln\frac{V_2}{V_1} \] पद 3: विस्तृत व्याख्या
Given: \[ n=2 \] \[ V_1=10L,\;V_2=100L \] So: \[ \Delta S=2R\ln\frac{100}{10} \] \[ =2R\ln10 \] \[ =2R(2.303) \] \[ =4.606R \] Surroundings: \[ \Delta S_{surroundings}=0 \] because no heat exchange.
पद 4: अंतिम उत्तर
अतः सही विकल्प (B) है।
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