Q.Describe the characteristics of an adiabatic process for an ideal gas. Explain, without detailed calculation, why an adiabatic curve on a $P$-$V$ diagram is always steeper than an isothermal curve passing through the same point.

In an adiabatic process, no heat at all enters or leaves the system ($Q=0$) throughout, either because the system is thermally insulated, or because the process happens too fast for appreciable heat exchange to occur. The equation satisfied by an ideal gas in a reversible adiabatic process is $PV^{\gamma}=\text{constant}$, where $\gamma = C_p/C_v > 1$.

The adiabatic curve is always steeper than the isothermal curve $PV=\text{constant}$ through the same point, because along the isothermal curve heat is continuously flowing IN from the reservoir as the gas expands, which keeps the temperature (and hence the pressure at any given volume) from falling as fast as it otherwise would; along the adiabatic curve, by contrast, no heat arrives at all, so the gas's own temperature genuinely falls as it expands and does work at its own expense, and a cooler gas at a given volume exerts noticeably less pressure -- ca …

State the defining condition ($Q=0$) and equation, then explain the steepness comparison in terms of temperature staying fixed (isothermal …

• Stating the adiabatic equation as $PV=\text{constant}$ (the isothermal equation) instead of $PV^{\gamma}=\text{constant}$. …