Two moles of an ideal gas undergo free expansion from 10 L to 100 L at 300 K. The values of ΔSsystem and ΔSsurroundings are (R is universal gas constant)

The correct answer is Option 4. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Chemistry Q59 – NEET-UG 2026

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Home Chemistry Chemical ThermodynamicsQuestion #312

Two moles of an ideal gas undergo free expansion from

10 L

100 L

300 K

. The values of

Δ S_{system}

and

Δ S_{surroundings}

are (R is universal gas constant)

Clue 1 of 3: Entropy Change for Ideal Gas

Entropy is a measure of the disorder or randomness of a system. For an ideal gas, entropy change depends on changes in volume and temperature.

🥷

Ninja Strategy•Free Expansion Properties

Recognize that free expansion of an ideal gas is an irreversible process where $Δ S_{system} > 0$ and $q_{surroundings} = 0$ , leading to $Δ S_{surroundings} = 0$ .

🧠 Full Solution Path

Step 1: Calculate

Δ S_{system}

for isothermal expansion✦ Active

For an ideal gas undergoing isothermal expansion, the entropy change of the system is given by the formula $Δ S_{system} = n R \ln (\frac{V_{2}}{V_{1}})$ . Given $n = 2$ moles, $V_{1} = 10 L$ , and $V_{2} = 100 L$ .

Δ S_{system} = 2 R \ln (\frac{100 L}{10 L}) = 2 R \ln (10)

Δ S_{system} = 2 R \times 2.303 = 4.606 R

Step 2: Calculate

Δ S_{surroundings}

for free expansion○ Expand

Free expansion implies that the external pressure is zero ( $P_{ext} = 0$ ). For an ideal gas, this means no work is done ( $W = 0$ ) and no heat is exchanged with the surroundings ( $q = 0$ ). Therefore, the heat absorbed by the surroundings ( $q_{surroundings}$ ) is zero.

Δ S_{surroundings} = \frac{q_{surroundings}}{T_{surroundings}} = \frac{0}{300 K} = 0

💡 Teacher's Secret Hint

Remember that for a free expansion of an ideal gas, $q = 0$ for the system, and thus $q_{surroundings} = 0$ .

Step 3: Combine the results○ Expand

Based on the calculations, $Δ S_{system} = 4.606 R$ and $Δ S_{surroundings} = 0$ . This corresponds to option (4).

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Chemistry Question 59 – NEET-UG 2026

Clue 1 of 3: Entropy Change for Ideal Gas

🧠 Full Solution Path