Question

At which of the following temperature would the molecules of a gas have twice the average kinetic energy they have at ${20}^{o}C$

• A. ${40}^{o}C$
• B. ${80}^{o}C$
• C. ${313}^{o}C$
• D. ${586}^{o}C$

Answer 1

The correct option is C ${313}^{o}C$

Given,

$E_2=2E_1$

$T_1={20}^{0}C$

Kinetic energy is

$E=\frac{3}{2}{K}_{B}T$

Here,

$E\propto T$

$\frac{E_1}{E_2}=\frac{T_1}{T_2}$

Substitute all value in above equation

$\frac{E_1}{2E_1}=\frac{(273+20)}{T_2}{T}_2=2\times 293=586K{T}_2=586-273={313}^{0}C$

Correct option is C