For adiabatic expansiion of a perfect gas, `(dP)/(P)` is

Options

A. `(dV)/(V)`
B. `gamma.(dV)/(V)`
C. `-gamma(dV)/(V)`
D. `-gamma^(2)(dV)/(V)`

Explanation

To solve the problem of finding \(\frac{dP}{P}\) for the adiabatic expansion of a perfect gas, we can follow these steps:

### Step 1: Understand the relationship for adiabatic processes
For an adiabatic process involving a perfect gas, the relationship between pressure \(P\), volume \(V\), and the adiabatic index \(\gamma\) (which is the ratio of specific heats, \(C_p/C_v\)) is given by:
\[ PV^\gamma = \text{constant} \]

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