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  • A gas undergoes an isothermal expansion process at a temperature of 400 K, during which it does 300 J of work. Calculate the change in entropy (S) of the gas during this process. Given that

A gas undergoes an isothermal expansion process at a temperature of 400 K, during which it does 300 J of work. Calculate the change in entropy (S) of the gas during this process.
Given that the ideal gas constant R = 8.314 J/mol · K and the number of moles of gas n = 0.05 mol.

Option: 1

0.75 \mathrm{~J} / \mathrm{k}


Option: 2

1.70 \mathrm{~J} / \mathrm{k}


Option: 3

20.20 \mathrm{~J} / \mathrm{k}


Option: 4

6.20 \mathrm{~J} / \mathrm{k}


Answers (1)

best_answer

The change in entropy of a gas during an isothermal process can be calculated using the equation:

\mathrm{\Delta S=\frac{Q}{T}}

where ?S is the change in entropy, Q is the heat added or removed, and T is the temperature.
Given that the gas does 300 J of work and the process is isothermal at T = 400 K, we can calculate ?S:

\mathrm{\Delta S=\frac{Q}{T}=\frac{300 \mathrm{~J}}{400 \mathrm{~K}}=0.75 \mathrm{~J} / \mathrm{K}}

Next, we know that for an ideal gas, the change in entropy during an isothermal process can also be calculated using the formula:

\mathrm{\Delta S=n R \ln \left(\frac{V_f}{V_i}\right)}

Given that n = 0.05 mol, R = 8.314 J/mol·K, and the process is isothermal, we can rearrange the formula and solve for the volume ratio:

\mathrm{\ln \left(\frac{V_f}{V_i}\right)=\frac{\Delta S}{n R}}

Substitute the values and solve for\mathrm{\frac{V_f}{V_i}:}

\mathrm{\begin{gathered} \frac{V_f}{V_i}=e^{\frac{\Delta S}{\mathrm{n} R}}=e^{\frac{0.75 \mathrm{~J} / \mathrm{K}}{0.05 \mathrm{~mol} \times 8.314 \mathrm{~J} / \mathrm{mol}-\mathrm{K}}} \\ \frac{V_f}{V_i} \approx 1.0703 \end{gathered}}

Therefore, the change in entropy of the gas during the isothermal expansion process is approximately
0.75 J/K. Therefore, the correct option is A.

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Rishi

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