Chemistry - Thermodynamics - I Question with Solution | TestHub

Explain the question: Find the volume change $\Delta \mathrm{V}$ in L during a system expansion. Concept: First Law: $\Delta \mathrm{U}=\mathrm{q}+\mathrm{w}$ and expansion work: $\mathrm{w}=-{\mathrm{P}}_{\text{ext }}\Delta \mathrm{V}$.

Solution:

Using standard IUPAC sign conventions (heat absorbed by the system is positive), we substitute the given values $\Delta \mathrm{U}=+300\mathrm{J}$ and $\mathrm{q}=+400\mathrm{J}$ into the first law of thermodynamics to determine work done:

$$\mathrm{w}=\Delta \mathrm{U}–\mathrm{q}=300\mathrm{J}–400\mathrm{J}=–100\mathrm{J}$$

The work done during expansion against a constant external pressure is $\mathrm{w}=–{\mathrm{P}}_{ext}\Delta \mathrm{V}$. By setting $-100\mathrm{J}=–(0.5\mathrm{bar})\Delta \mathrm{V}$ and applying the conversion factor $1\mathrm{bar}\cdot \mathrm{L}=100\mathrm{J}$, we rewrite the equality as $1\mathrm{bar}\cdot \mathrm{L}=0.5\mathrm{bar}\cdot \Delta \mathrm{V}$.

Solving for the unknown variable, we obtain $\Delta \mathrm{V}=\frac{1}{0.5}=2\mathrm{L}$.

Final Answer: 2