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

Concept:
For an ideal gas, mean kinetic energy is directly proportional to absolute temperature: \[ \bar{K}\propto T \] ip

Step 1: Convert the given temperature into Kelvin.
\[ 399^\circ\text{C}=399+273=672\text{ K} \] ip

Step 2: Find the new temperature for energy \(E/2\).
Since energy becomes half, \[ T_2=\frac{672}{2}=336\text{ K} \] ip

Step 3: Convert back into Celsius.
\[ T_2=336-273=63^\circ\text{C} \] ip Hence, the correct answer is:
\[ \boxed{(D)\ 63^\circ\text{C}} \]