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  • A piston-cylinder system contains 1 mol of an ideal gas initially at a pressure of 2 atm and a temperature of 300 K. The gas undergoes a reversible isothermal expansion against a constant external

A piston-cylinder system contains 1 mol of an ideal gas initially at a pressure of 2 atm and a temperature of 300 K. The gas undergoes a reversible isothermal expansion against a constant external pressure of 1 atm until the volume is doubled. Calculate the change in entropy of the gas during this process.

Given:   

The ideal gas constant \mathrm{(R) \text { is } 8.314 \mathrm{~J} /(\mathrm{mol \; K})}

Option: 1

3.478 J/K


Option: 2

5.749 J/K


Option: 3

8.254 J/K


Option: 4

4.251 J/K


Answers (1)

best_answer

Step 1: Calculate the initial volume of the gas using the ideal gas law:

                         \mathrm{V=\frac{n R T}{P}}

Substitute the given values:

                    \begin{gathered} \text{V}=\frac{1 \mathrm{~mol} \cdot 8.314 \mathrm{~J} /(\mathrm{mol} \mathrm{K}) \cdot 300 \mathrm{~K}}{2 \mathrm{~atm}} \\ \text{V}=12471 \mathrm{~L} \end{gathered}

Step 2: Calculate the final volume after the expansion: The volume of the gas is doubled during the expansion, so the final volume is  \mathrm{2 \times 12471\: L = 24942\: L.}
Step 3: Calculate the change in entropy using the ideal gas law:

                         \mathrm{\Delta S=n R \ln \left(\frac{V_{\text {final }}}{V_{\text {initial }}}\right)}

Substitute the calculated values:

                         \mathrm{\Delta S=1 \mathrm{~mol} \cdot 8.314 \mathrm{~J} /(\mathrm{molK}) \cdot \ln \left(\frac{24942 \mathrm{~L}}{12471 \mathrm{~L}}\right)}

Calculate the natural logarithm term:

                       \mathrm{\ln \left(\frac{24942 L}{12471 L}\right)=\ln (2) \approx 0.693}

Substitute the value and calculate \mathrm{\Delta S}:

                       \begin{gathered} \mathrm{\Delta S}=1 \mathrm{~mol} \cdot 8.314 \mathrm{~J} /(\mathrm{molK}) \cdot 0.693 \\ \mathrm{\Delta S} \approx 5.749 \mathrm{~J} / \mathrm{K} \end{gathered}

Final Answer:

The change in entropy of the gas during the reversible isothermal expansion process is approximately 5.749 J/K.

So, correct option is (2).

Posted by

chirag

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