Question

Read the given statements and decide which is/are correct on the basis of kinetic theory of gases
(1) Energy of one molecule at absolute temperature is zero.
(2) rms speeds of different gases are same at same temperature.
(3) For one gram of all ideal gases, kinetic energy is same at same temperature.
(4) For one mole of all ideal gases, mean kinetic energy is same at same temperature.

(A) All are correct
(B) 1 and 4 are correct
(C) 4 is correct
(D) None of these

Answer 1

Hint:First go through the postulates of the kinetic theory of gases. Here try to use the method of elimination in the given option above in the question. Check each and every option one by one whether it is correct or not and then eliminate the wrong answer. Finally, you will get the required answer to the question given. All the options are related to kinetic energy.


Formula used:
The average kinetic energy is
$K = \dfrac{1}{2}m \times \dfrac{{3RT}}{M}$


Complete answer:
Let's start with the method of elimination:
Statement (1):
From the kinetic theory of gases we know that;
The energy of one molecule of gas can never be zero. If the gas isn't ideal, its molecules will have potential energy. As a result, statement (I) is incorrect.
Statement(2):
We know,
$v_{rms}\varpropto~\frac{1}{\sqrt{M}}$
The RMS speed of different gases at the same temperature is determined by their molecular weight. As a result, statement (II) is also incorrect.
Statement (3):
We know,
$E_{gm}\varpropto~\frac{1}{M}$
The kinetic energy of one gram of gas is proportional to its molecular weight.
As a result, statement (III) is also incorrect.
Statement (4):
$E=\frac{3}{2}RT$
However, the K.E. of one mole of an ideal gas is the same at the same temperature.
. As a result, (IV) is correct.
The correct option(C).



Note: A gas particle's average kinetic energy is directly proportional to its temperature. The speed of the gas molecules increases as the temperature rises. A gas's kinetic energy is a measurement of its Kelvin temperature. Individual gas molecules move at different speeds, but the gas's temperature and kinetic energy are based on the average of these speeds.