Question

The kinetic energy of a mole of ideal gas in calories is approximately equal to ___.

(A) 3 times its absolute temperature

(B) 2 times its absolute temperature

(C) 4 times its absolute temperature

(D) 2/3 times its absolute temperature

Answer 1

Hint: Kinetic energy of an ideal gas is given by the formula, $K.E.=\dfrac{3}{2}nRT$. According to the given options we need to find kinetic energy for one mole of ideal gas in terms of temperature. Just substitute the value of gas constant, R in calories and then find the answer.

Complete step by step solution:

- Kinetic energy is the energy required by an object in motion.

- According to the question, we need to find the value of kinetic energy in calories for one mole of an ideal gas.

- Kinetic energy is given as, $K.E.=\dfrac{3}{2}nRT$ where n is the number of moles, T is the temperature and R is the universal gas constant which is $R=1.9872 cal{{K}^{-1}}mo{{l}^{-1}}$.

- Substituting these values we get,

\[K.E.=\dfrac{3}{2}\times 1\times 1.9872\times T\]

- Now, the value of the universal gas constant, R, is approximately equal to 2. Therefore, kinetic energy becomes, $K.E.=\dfrac{3}{2}{{}}\times 1.9872 \times T=3 Tcal$ (Now since R 2cal k^-1mol^-1)

- Therefore, kinetic energy for a mole of ideal gas in calories is approximately equal to three times its absolute temperature.

Therefore, the answer is option A.

Additional Information: 

The kinetic theory of gases is based on the following postulates:

Gases have small molecules which are spread far apart. The volume occupied by gas molecules is mostly free space.

Gas molecules are always in a constant state of motion.

They collide with each other and with the walls of the container. Collisions with the wall of the container gives rise to the pressure of the gas.

The collisions are said to be perfectly elastic as the gas molecules do not lose any kinetic energy during collisions.

The total kinetic energy of the gas molecules remains constant unless an external force acts on it.

Note: Remember for an ideal gas, kinetic energy is given by the formula, $K.E.=\dfrac{3}{2}nRT$ where n is the number of moles, T is the temperature and R is the universal gas constant having the value as $R=8.314J{{K}^{-1}}mo{{l}^{-1}}=1.9872cal{{K}^{-1}}mo{{l}^{-1}}$.