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The average kinetic energy of hydrogen molecules at 300 K is E. At the same temperature the average kinetic energy of oxygen molecules will be
$ E \alpha T $
The temperature at which the average translational kinetic energy of a molecule is equal to the energy gained by an electron accelerating from rest through a potential differencc of 1 volt is
$ { 3 \over 2 } k_B T = 1 eV \Rightarrow T = { 2 \over 3 } { eV \over k_B} = {2 \over 3 } \times { 1.6 \times 10^{-19} \over 1.38 \times 10^{-23} } = 7.7 \times 10^3 K $
At a given temperature the rms velocity of molecules of the gas is
$ \nu _{rms } = \sqrt {3RT \over M_o } \Rightarrow \nu _{rms} \alpha { 1 \over \sqrt {M_o} } $
According to the kinetic theroy of gases the r.m.s velocity of gas molecules is directly proportional to
$ \nu_{rms } \alpha \sqrt T $
The speeds of 5 molecules of a gas (in arbitrary units) are as follows: 2, 3, 4, 5, 6, The root mean square speed for these molecules is
$ \nu_{rms} = \sqrt { \nu_1^2 + \nu_2^2 + \nu_3^2 + \nu_4^2 + \nu_5^2 \over 5 } = 4.24 $
To what temperature should the hydrogen at room temperature ($ 27 ^\circ C$ ) be heated at constant pressure so that the rms velocity of its molecule becomes double of its previous value
$ \nu_{rms } \alpha \sqrt T \Rightarrow { (\nu_{rms})_2 \over (\nu_{rms})_1} = \sqrt {T_2 \over T_1} $
Root mean square velocity of a molecule is $ \nu $ at pressure P. If pressure is increased two times, then the rms velocity becomes
rms velocity does not depend on pressure.
The rms speed of gas molecules is given by
$ \nu _{rms } = \sqrt { 3RT \over M_o} = \sqrt {3} \sqrt { RT \over M_o } = 1.73 \sqrt { RT \over M_o} $
A sample of gas is at $ 0 ^\circ C$ . To what temperature it must be raised in order to double the rms speed of molecule.
$ \nu_{rms} \alpha \sqrt T $ To double the rms speed temperature should be made four times i.e. $ \therefore T_2 = 4 T_1 $
If the ratio of vapour density for hydrogen and oxygen is 1/ 16 , then under constant pressure the ratio of their rms velocities will be
$ \nu _ {rms} =\sqrt { 3P \over \rho } \Rightarrow { \nu_1 \over \nu_2 } = \sqrt { \rho_2 \over \rho_1} = \sqrt { 16 \over 1} = 4:1 $
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.