Question

For any monoatomic gas the quantity / quantities independent of the nature of the gas at the same temperature is/are :

• A. The number of molecules in one mole
• B. The number of molecules in equal volume and pressure
• C. The translational kinetic energy of one mole
• D. The kinetic energy of unit mass

Answer 1

Answer: (A), (B), (C)

The correct options are
A The number of molecules in one mole
B The number of molecules in equal volume and pressure
C The translational kinetic energy of one mole

For monoatomic gas
given, $T$ = same/constant
(A) The number of molecules in one mole is equal to avogadro’s number
$N_A=6.023\times {10}^{23}$
(B) Number of moles
$PV=nRT$
$n=\frac{PV}{RT}$
For same $P,V\text{and}T$
n is same
(C) For monoatomic gas KE is only the function of temperature
K.E. = $f\left(T\right)$
For monatomic gas
Translational kinetic energy of n moles
$KE=\frac{3nRT}{2}$ [same]
(D) mole $\left[n\right]=\frac{m}{M}$
Unit mass contains different no. of moles
$KE=\frac{3}{2}nRT$
Hence for any monoatomic gas kinetic energy per unit mass is different. Options (A), (B), (C) are correct