Question

Calculate the final

pressure of a sample of
water vapour That expands reversibily and
adiabaticaly from 8.73 toir at 500 cm³ to a
final volume 3dm³ take gamma 1.3.

Answer 1

To solve this problem, we can use the adiabatic process equation:

P₁V₁^γ = P₂V₂^γ

Where:
P₁ = initial pressure
V₁ = initial volume
P₂ = final pressure (what we want to find)
V₂ = final volume
γ = specific heat ratio (given as 1.3)

Converting the initial volume to cubic meters (m³) for consistency:

V₁ = 500 cm³ = 0.5 dm³

And converting the final volume to cubic centimeters (cm³) for ease of calculation:

V₂ = 3 dm³ = 3,000 cm³

Substituting the values into the equation, we get:

P₁V₁^γ = P₂V₂^γ

P₂ = P₁V₁^γ / V₂^γ

P₂ = (8.73 kPa) x (0.5 dm³)^1.3 / (3,000 cm³)^1.3

P₂ = 1.62 kPa

Therefore, the final pressure of the water vapor is 1.62 kPa.