Question

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27°C is

• A. 327°C
• B. 627°C
• C. 927°C
• D. 1227°C

Answer 1

The Correct Option is A

The average kinetic energy (\( KE \)) of gas molecules is directly proportional to the absolute temperature (\( T \)) and is given by: \[ KE = \frac{3}{2} k T, \] where \( k \) is Boltzmann's constant. \bigskip 
Step 1: Initial kinetic energy at \( 27^\circ \text{C} \). The absolute temperature at \( 27^\circ \text{C} \) is: \[ T_1 = 27 + 273 = 300 \, \text{K}. \]
Step 2: New temperature for double kinetic energy. If the kinetic energy becomes double: \[ KE_2 = 2 \cdot KE_1. \] Since \( KE \propto T \): \[ T_2 = 2 \cdot T_1 = 2 \cdot 300 = 600 \, \text{K}. \] Convert \( T_2 \) to Celsius: \[ T_2 = 600 - 273 = 327^\circ \text{C}. \] 
Final Answer: The temperature is: \[ \boxed{327^\circ \text{C}}. \]