During an adiabatic expansion, volume increases to 8 times and temperature reduces to 1/4th. Find the adiabatic constant γ.

Solution:

For adiabatic process:

TV^γ-1 = constant

Given:

• V₂ = 8V₁
• T₂ = T₁/4

Using formula:

T₁V₁^γ-1 = T₂V₂^γ-1

T₁ = (T₁/4)(8V₁)^γ-1

1 = (1/4) × 8^γ-1

4 = 8^γ-1

2² = (2³)^γ-1

2 = 3(γ - 1)

γ - 1 = 2/3

γ = 5/3

Answer: γ = 5/3