When an ideal gas is compressed adiabatically and reversibly, what is the final temperature?

When an ideal gas is compressed adiabatically and reversibly, its temperature increases because no heat is exchanged with the surroundings, and all the work done on the gas increases its internal energy.

Formula used:

T₂ / T₁ = (V₁ / V₂)^(γ − 1)

Where:

• T₁ = initial temperature
• T₂ = final temperature
• V₁, V₂ = initial and final volumes
• γ = Cp/Cv (heat capacity ratio)

Key Concept:

• During compression, volume decreases
• So, (V₁ / V₂) > 1
• Therefore, T₂ > T₁

Conclusion:

• Final temperature depends on the compression ratio and γ
• It is always higher than the initial temperature in adiabatic compression

Key Takeaway:

In reversible adiabatic compression, temperature rises according to:
T₂ = T₁ × (V₁ / V₂)^(γ − 1)