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 on the gas during this expansion?

Question

Quizplus · Accepted Answer

The work done on a gas during expansion can be calculated as the area under the pV curve. Since the pressure increases linearly with volume, the area under the curve is a trapezoid. The formula for the work done (W) in such a process is W = (P1 + P2)/2 * ΔV, where P1 and P2 are the initial and final pressures, and ΔV is the change in volume. Substituting the given values: W = (110 kPa + 225 kPa)/2 * (0.085 m^3 - 0.040 m^3) = 167.5 kPa * 0.045 m^3 = 7.5375 kJ. Since work done on the gas is considered positive and work done by the gas is considered negative in this context, the correct answer is -7.5 kJ, indicating that work is done by the gas.

A Gas Expands from an Initial Volume of 0