An ideal gas having initial pressure P, volume Vand temperature T is allowed to expand adiabatically until its volume becomes 5.66 V while the temperature falls to T/2. How many degrees of freedom do the gas molecule have ?

Explanation

To solve the problem step-by-step, we will follow the reasoning outlined in the video transcript.

### Step 1: Understand the adiabatic process
In an adiabatic process, the relationship between pressure (P), volume (V), and temperature (T) of an ideal gas is given by the equation:
\[ PV^{\gamma} = \text{constant} \]
where \( \gamma \) (gamma) is the heat capacity ratio, defined as:
\[ \gamma = \frac{C_p}{C_v} = 1 + \frac{2}{f} \]
where \( f \) is the degrees of freedom of the gas molecules.
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