Question

The pressure exerted by an ideal gas is `P = (1)/(3) (M)/(V)C^(2)`, where the symbols have their usual meaning. Using standard gas equation, PV = RT, we find that `C^(2) = (3 RT)/(M) or C^(2) oo T`. Average kinetic energy of translation of one mole of gas ` =(1)/(2) MC^(2) = (3 RT)/(2)` with the help of the passage given above, choose the most appropriate alternative for each of the following quetions :
Average thermal energy of a helium atom at room temperature `(27^(@)C)` is Given, Boltzmann constant `k = 1.38 xx 10^(-23) JK^(-1)` :
A. `2.61 xx 10^(21) J`
B. `6.21 xx 10^(21) J`
C. `6.21 xx 10^(-21) J`
D. `6.21 xx 10^(-23) J`

Answer 1

Correct Answer - C
Here, `T = 27^(@)C = 27+273 = 300K`
`k=1.38 xx 10^(23)jK^(-1)`
Average thermal energy of helium atom
`=3/2 kT = 3/2 xx 91.38 xx 10^(-23) xx 300`
`=6.21 xxx 10^(-21)J`.