The temperature and pressure of one mole of an ideal monoatomic gas changes from `25^(@)` C and 1 atm pressure to `250^(@)` C and 25 atm. Calculate the change in entropy for the process.

Explanation

To calculate the change in entropy (\( \Delta S \)) for the process where one mole of an ideal monoatomic gas changes from \( 25^\circ C \) and 1 atm pressure to \( 250^\circ C \) and 25 atm, we can use the formula:

\[ \Delta S = n C_P \ln \frac{T_2}{T_1} + n R \ln \frac{P_1}{P_2} \]

### Step 1: Convert temperatures from Celsius to Kelvin
- \( T_1 = 25^\circ C = 25 + 273 = 298 \, K \)
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