Q4. A monatomic ideal gas (γ = 5/3) at 400 K expands reversibly and adiabatically to twice its volume, with constant γ. Find its final temperature.
TVγ−1 = constant, so T2 = 400 × (1/2)2/3, about 252 K.
Q5. A gas at a constant 1.5 × 10 Pa expands from 2.5 L to 4.0 L. How much work does it do?
W = P(V2 − V1) = 1.5 × 10 × 1.5 × 10 = 225 J.
Q6. Why is the adiabatic curve through a point on a P–V graph steeper than the isotherm through the same point?
In an adiabatic expansion the temperature falls as well as the volume rising, so the pressure drops faster than in an isothermal expansion, where only the volume changes. Mathematically, the slope dP/dV is −γP/V for the adiabatic and −P/V for the isotherm, and γ > 1.