An ideal gas undergoes an isothermal expansion from 1text dm ^3 to 10text dm ^3 at 300text K against a constant external pressure of 1text bar . Determine the change in entropy of the surroundings (Delta S_ surr ) in text J K ^ -1 .

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EEJ MAIN Chemistry QUESTION #7134

Question 1

An ideal gas undergoes an isothermal expansion from $1\text{ dm}^3$ to $10\text{ dm}^3$ at $300\text{ K}$ against a constant external pressure of $1\text{ bar}$. Determine the change in entropy of the surroundings ($\Delta S_{surr}$) in $\text{J K}^{-1}$.

$3.0$
$-3.0$✔️
$2.5$
$-2.5$

Correct Answer Explanation

In an irreversible expansion against constant external pressure, the work done by the gas is $w = -P_{ext}\Delta V = -1 \text{ bar} \times (10 - 1) \text{ dm}^3 = -900\text{ J}$. For an isothermal process of an ideal gas, $\Delta U = 0$, so $q_{sys} = -w = 900\text{ J}$. The heat gained by the surroundings is $q_{surr} = -q_{sys} = -900\text{ J}$. Thus, $\Delta S_{surr} = \frac{q_{surr}}{T} = \frac{-900}{300} = -3.0\text{ J K}^{-1}$.

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