A gas is compressed isothermally to one-third of its initial volume.
Initial volume:
V₀ = 3 L
Bulk modulus of the gas is:
B = 3 × 105 N/m²
Find the magnitude of work done on the gas.
For an isothermal process:
Bulk modulus:
B = P
Therefore:
Initial pressure:
P = 3 × 105 Pa
Initial volume:
V₁ = 3 L
= 3 × 10−3 m³
Final volume:
V₂ = V₁/3
= 10−3 m³
Work done during isothermal compression:
W = PV₁ ln(V₁/V₂)
= (3 × 105) (3 × 10−3) ln(3)
= 900 × 1.0986
≈ 989 J
Final Answer
989 J