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  • A sample of 5 mol of an ideal gas is initially at a pressure of 4 atm and a temperature of 350 K. The gas is subjected to an irreversible heating process at constant pressure until its tempe

A sample of 5 mol of an ideal gas is initially at a pressure of 4 atm and a temperature of 350 K. The gas
is subjected to an irreversible heating process at constant pressure until its temperature reaches 450 K.
Calculate the change in entropy of the gas during this process.
Given:
• The molar heat capacity at constant pressure (Cp) for the gas is 30 \mathrm{~J} /(\mathrm{mol} \mathrm{K})

Option: 1

45.4 \mathrm{~J} / \mathrm{K}


Option: 2

47.6 \mathrm{~J} / \mathrm{K}


Option: 3

37.7 \mathrm{~J} / \mathrm{K}


Option: 4

33.2 \mathrm{~J} / \mathrm{K}


Answers (1)

best_answer

Step 1:Calculate the initial and final entropies using the formula:

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

Substitute the values:

\mathrm{\Delta S=5 \mathrm{~mol} \cdot 30 \mathrm{~J} /(\mathrm{mol} \mathrm{K}) \cdot \ln \left(\frac{450 \mathrm{~K}}{350 \mathrm{~K}}\right)}

Step 2: Calculate the natural logarithm term:
\mathrm{\ln \left(\frac{450 \mathrm{~K}}{350 \mathrm{~K}}\right) \approx 0.2513}

Step 3: Calculate ?S:

\mathrm{\begin{gathered} \Delta S=5 \mathrm{~mol} \cdot 30 \mathrm{~J} /(\mathrm{mol} \mathrm{K}) \cdot 0.2513 \\ \Delta S \approx 37.7 \mathrm{~J} / \mathrm{K} \end{gathered}}

The change in entropy of the gas during the irreversible heating process is approximately
\mathrm{37.7 \mathrm{~J} / \mathrm{K}}
So, option C is correct

Posted by

Riya

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