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Chemistry · THERMODYNAMICS
हिन्दीA sample of \( 0.5\text{ mol} \) of an ideal gas expands into an evacuated chamber of volume \( 20\text{ L} \) from an initial volume of \( 5\text{ L} \) at \( 300\text{ K} \). Subsequently, \( 150\text{ J} \) of work is done on the gas while compressing it back to \( 10\text{ L} \) at constant volume, and \( 50\text{ J} \) of heat is removed. What is the overall change in internal energy (\( \Delta U \))?
Correct answer · Option B
\( +100\text{ J} \)
Explanation
In free expansion into vacuum, \( p_{\text{ex}} = 0 \implies w_1 = 0 \), and isothermal \( \Delta U_1 = 0 \). In the next step, \( w_2 = +150\text{ J} \) and \( q_2 = -50\text{ J} \), so \( \Delta U_2 = q_2 + w_2 = -50 + 150 = +100\text{ J} \). Thus overall \( \Delta U = +100\text{ J} \).
