Gas Pressure and PV diagram

Question

A gas undergoes two processes. In the first the volume remains constant at 0.3m³ and the pressure decreases from 5.00 × 10⁵ Pa to 1.00 × 10⁵ Pa. The second process is an expansion to a volume of 0.35m at 1.00 × 10⁵ Pa.

a) How can I sketch a PV diagram showing both processes?

b) How do I find the total work done by the gas during both processes?

Answer 1

a) The first process is a constant Volume process which is a vertical line on a PV diagram from 1st Pressure to second Pressure (P on y, Von x)

The second process is a horizontal line going from .3 to .35 m³ at constant pressure of 1 Bar (100,000 Pa)

Generally, the work done by the gas is the integral of PdV from V₁ to V₂. It is the signed area under the curve of P vs. V. In this case W=0 for a constant V process. W = P(V₂-V₁) for a constant pressure process. If you use Pascals for pressure and m³ for volume, you get Joules for work due to the nice properties of the MKS system.

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