Question

A container holds 2.7 mol of gas. The total average kinetic energy of the gas molecules in the container is equal to the kinetic energy of a 8.5x10-3 kg bullet with a speed of 880 m/s. What is the Kelvin temperature of the gas?

Answer 1

Solution:

Mass of the bullet (m)= 8.5× 10-3 Kg

Speed of the bullet (v) = 880 m/s

Kinetic energy of the bullet (E)= (1/2)×mv2

= (1/2)× 8.5× 10-3×(880)2= 3291.2 joule

The total average kinetic energy of the gas molecules (k)= kinetic energy of the bullet = 3291.2 joule/mol

Average kinetic energy of the gas molecules is

Where

R= universal gas constant = 8.314 j/mol.k

T =Temperature in kelvin

So

Or, T = (2×3291.2)/(3× 8.314) = 263.9 Kelvin

The Kelvin temperature of the gas is 263.9 Kelvin