Discussion
Adiabatic bulk modulus of a substance is defined as
Answer: D
The adiabatic bulk modulus is \(-v\left(\frac{\partial P}{\partial v}\right)_{s}\).
A bulk modulus measures the pressure increase needed per fractional decrease in volume, \(K = -v\frac{\partial P}{\partial v}\), with the minus sign making it positive because volume falls as pressure rises. 'Adiabatic' for a reversible process means constant entropy, so the derivative is taken at constant \(s\).
\(-v(\partial P/\partial v)_{T}\) is the isothermal bulk modulus. The forms \(-\frac{1}{v}(\partial v/\partial P)\) are compressibilities, the reciprocals of bulk moduli: isothermal at constant \(T\) and isentropic at constant \(s\).
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