For an adiabatic process involving an ideal gas, which quantity is constant?
A$PV$
B$P + V$
C$PV^\gamma$
D$P/V$
Answer & Solution
Correct answer: C. $PV^\gamma$
Adiabatic process means no heat exchange ($dQ = 0$). The first law plus the ideal-gas equation give $PV^\gamma = \text{constant}$, where $\gamma = C_p / C_v$ is the adiabatic index (about $1.4$ for diatomic gases, $5/3$ for monoatomic).
Option A ($PV = $ constant) is the isothermal law, not the adiabatic one. The exponent $\gamma > 1$ is what makes adiabatic curves steeper than isothermal curves on a $P$-$V$ diagram.
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