Question

A certain ideal gas has molar heat capacity at constant volume CV. A sample of this gas initially occupies a volume V0 at pressure p0 and absolute temperature T0. The gas expands isobarically to a volume 2V0, then expands further adiabatically to a final volume of 4V0.
Draw a PV diagram for the squence of process.

Answer 1

Answer:

Explanation:

The processes are described on the image attached below. The isobaric process consists of an horizontal line, the adiabatic expansion is described by a polytropic curve:

$P_{2} \cdot V_{2}^{\gamma} = P_{3} \cdot V_{3}^{\gamma}$

Where:

$\gamma = \frac{c_{p}}{c_{v}}$

$\gamma = 1 + \frac{R}{c_{v}}$

Final pressure is:

$P_{3} = P_{2}\cdot \left(\frac{V_{2}}{V_{3}} \right)^{\gamma}$

$P_{3} = P_{o}\cdot \left(\frac{1}{2}\right)^{\gamma}$

$P_{3} = \frac{P_{o}}{2^{\gamma}}$