Question

The kinetic energy of one gram of argon gas at 27⁰c will be
1. 4000 J
2. 4180 J
3. 4739.5 J
4. 3739.5 J
5.

Answer 1

Correct Answer - Option 4 : 3739.5 J

Correct option-4

Concept:

• The kinetic theory is a very important concept as it can be used to describe many macroscopic properties of gases.
• For one thing, we can use the kinetic theory to derive the average translational kinetic energy of a gas molecule inside a container
• It turns out that the average translational kinetic energy of molecules depends strictly on the temperature of the system.
• In other words, as the average translational kinetic energy of the molecules within a gaseous system increases, so does the temperature.
• The total translational kinetic energy of one mole of an ideal gas is given by-

\(K.E=\frac{3}{2}kT\)

Where,

k = Boltzmann constant

T = temperature in kelvin.

Calculation:

Given:-

T = 27⁰c = 300k

m = 1gm

R = 8.31J/molk

K.E per gram molucule of oxygen = (3/2) RT

\(\Rightarrow K.E=\left ( \frac{3}{2}\times 8.31\times 300 \right )J\)

\(\therefore K.E=3739.5J\)

Hence, option-4 is correct