Question

The average kinetic energy per molecule of an ideal gas at \(27^\circ C\) is \(E\). The temperature of the gas at which the average kinetic energy per molecule will be \(2E\) is

• A. \(127^\circ C\)
• B. \(227^\circ C\)
• C. \(327^\circ C\)
• D. \(400^\circ C\)
• E. \(527^\circ C\)

Hint:

Always convert temperatures to Kelvin when working with temperature-related changes in kinetic energy, as Kelvin directly correlates with the thermal energy of a system.

Answer 1

The Correct Option is C

Step 1: Recall that the average kinetic energy (\(E\)) of an ideal gas is proportional to the absolute temperature (\(T\)). 
If \(E\) is doubled, the absolute temperature must also double. 
Step 2: Convert the initial temperature from Celsius to Kelvin: \(T_1 = 27^\circ C = 300 K\). 
Step 3: The new temperature in Kelvin when \(E\) doubles is \(2 \times 300 K = 600 K\). 
Step 4: Convert \(600 K\) back to Celsius: \(600 K - 273.15 = 326.85^\circ C\), which rounds to \(327^\circ C\).