Calculate the value of Boltzmann constant `k_(B)`, Given `R = 8.3 xx 10^(3) J//kg-mol-K` and Avogadro number, ` N = 6.03 xx 10^(26)//kg-mol`.

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to: [Boltzmann constant k _ B = 1.38 xx 10 ^( -23) J//K Avogadro Number N _ A = 6.02 xx 10 ^( 26) // Kg Radius of Earth : 6.4 xx 10 ^( 6 ) m Gravitational acceleration on Earth = 10 ms ^( -2) ]

Calculate the kinetic energy of one mole of argon at 127^(@)C . Given,Boltzmann's constant, k_(B) = 1.381 xx 10^(-23) J "molecular"^(-1) K^(-1) . Avogardro numbe, N = 6.02 xx 10^(23) "mol"^(-1)

The kinetic energy of a molecule of oxygen at 0^(@)C is 5.64 xx 10^(-21) J . Calculate Avogadro's number. Given R = 8.31 J "mol^(-1)K^(-1) .

The approximate number of air molecules in a 1 m^3 volume at room temperature (300 K) and atmospheric pressure is (Use R = 8.2 xx 10^(-5 ) m^3 atm/mol K and N_A =6.02 xx 10^(23) mol^(-1) )

Calculate the rms speed of smoke particles of mass 5 xx 10^(-17) kg in their Brownian motion in air at NTP. Given k_(B) = 1.38 xx 10^(-23) J//K

Calculate the average molecular kinetic energy : (a) per kilomole, (b) per kilogram, of oxygen at 27^@C . ( R = 8320 J/K mole K, Avogadro's number =6*03xx10^(26) molecules/K mole )