Question

The initial average kinetic energy of the molecules was E, when a gas sample is at 27$^\circ$C. When the gas is heated to 327$^\circ$C, then the final average kinetic energy will be ______.

• A. $\sqrt{2}E$
• B. 2E
• C. 300E
• D. 327E

Hint:

Always convert Celsius to Kelvin! A common trap is assuming that because $327$ isn't twice $27$, the energy doesn't double. Temperature formulas in physics almost universally demand the absolute thermodynamic scale.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The average kinetic energy of gas molecules is directly proportional to the absolute temperature (in Kelvin): $E \propto T$.

Step 2: Formula Application:
$T_1 = 27 + 273 = 300$ K. $T_2 = 327 + 273 = 600$ K.

Step 3: Explanation:
Since $T_2 = 2 \times T_1$, the average kinetic energy will also double. $E_2 / E_1 = T_2 / T_1 = 600 / 300 = 2$. $E_2 = 2E$.

Step 4: Final Answer:
The final average kinetic energy will be 2E.