A gas expands from an initial volume of 0.040 m³ to a final volume of 0.085 m³ while its pressure increases linearly with the volume (so that the process follows a straight-line path in a pV diagram)from 110 kPa to 225 kPa.How much work is done by the gas during this expansion? A)5.2 kJ B)7.5 kJ C)7.8 kJ D)11 kJ E)12 kJ

Question

Quizplus · Accepted Answer

The work done by the gas during a linear expansion in a pV diagram can be calculated as the area under the curve, which in this case is a trapezoid. The formula for the work done is $W = \frac{1}{2}(P_{\text{final}} + P_{\text{initial}}) \times (V_{\text{final}} - V_{\text{initial}})$. Substituting the given values, $W = \frac{1}{2}(225\,kPa + 110\,kPa) \times (0.085\,m^3 - 0.040\,m^3) = \frac{1}{2} \times 335\,kPa \times 0.045\,m^3 = 7.5375\,kJ$, which rounds to approximately 7.5 kJ.

A Gas Expands from an Initial Volume of 0