The thermodynamic property that measures the extent of molecular disorder is called entropy. Entropy change of phase transformation can be calculated using Trouton's formula `(DeltaS = DeltaH//T)`. In the reversible adiabatic process, however, `DeltaS` will be zero. the rise in temperature in isobaric and isochoric conditions is found to increase the randomness or entropy of the system.
`DeltaS = 2.303 C log (T_(1)//T_(2))`
When `1` mol of an ideal gas is compressed to half of its volume, its temperature becomes half. Then the change in entropy `(DeltaS)` would be

Options

A. `C_(V) In 4`
B. `C_(P) In 2`
C. `C_(V)R In4`
D. `(C_(V)-R)In 4 xx C_(P)`

Explanation

To solve the problem of calculating the change in entropy (ΔS) when 1 mole of an ideal gas is compressed to half its volume and its temperature becomes half, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Let the initial volume \( V_1 = x \).
- The final volume after compression is \( V_2 = \frac{x}{2} \).
- Let the initial temperature \( T_1 = T \).
...