Question

The mean kinetic energy of the molecules of an ideal gas at $399^\circ\text{C}$ is ' $E$ '. The temperature at which the mean kinetic energy of its molecules will be ' $E/2$ ', is

• A. $336^\circ\text{C}$
• B. $276^\circ\text{C}$
• C. $123^\circ\text{C}$
• D. $63^\circ\text{C}$

Hint:

Mean kinetic energy always follows Kelvin temperature, not Celsius temperature.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Kinetic energy of gas molecules is directly proportional to the absolute temperature in Kelvin.
Step 2: Key Formula or Approach:
$E \propto T \implies E_1/E_2 = T_1/T_2$.
Step 3: Detailed Explanation:
$T_1 = 399 + 273 = 672\text{ K}$.
$E_2 = E/2 \implies T_2 = T_1 / 2 = 672 / 2 = 336\text{ K}$.
Celsius temperature $= 336 - 273 = 63^\circ\text{C}$.
Step 4: Final Answer:
The temperature is $63^\circ\text{C}$.