In an adiabatic process, the First Law gives: dE = dW.
Use this result to determine adiabatic paths (adiabats) in the P-V diagram.
dE = dW → nCV dT = - P dV = - n RT dV/V.
→ CV dT/T = - R dV/V but R = (CP-CV).
dT/T = - (dV/V) [(CP-CV)/ CV].
→ d ln T = - (γ - 1) d ln V or d [ln T V (γ - 1)] = 0.
→ T V (γ - 1) = constant.
Equivalently use T ∝ PV
to give P V γ = constant.
Note: adiabats are steeper than
Note: adiabats are steeper than isotherms!