Question

A gas in a piston-cylinder assembly undergoes a process for which the relationship between pressure and volume is pV² = constant. The initial pressure is 1 bar, the initial volume is 0.1 m³, and the final pressure is 9 bar.

Determine:
a) Final volume, in m³
b) Do you expect V₂ to be higher or lower than ?
c) Work for the process, in kJ
d) For part b, does the sign of your answer make sense? Why or why not?

Answer 1

The final volume of the gas in the piston-cylinder assembly is approximately 0.033 m³.

Step-by-step explanation:

To determine the final volume of the gas in the piston-cylinder assembly, we can use the relationship between pressure and volume given by pV² = constant. We have the initial pressure, p₁ = 1 bar, and initial volume, V₁ = 0.1 m³. We also have the final pressure, p₂ = 9 bar. Substituting these values into the equation, we can solve for the final volume:

p₁V₁² = p₂V₂²

1 * 0.1² = 9 * V₂²

0.01 = 9 * V₂²

V₂² = 0.01/9

V₂ = √(0.01/9)

V₂ ≈ 0.033 m³

So the final volume is approximately 0.033 m³.