JEE PHYSICS MCQ: KINETIC THEORY OF GASES

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Application +4 | -1

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 \times {10^{ - 23}}J/K,

Avogadro number

{N_A} = 6.02 \times {10^{26}}/kg,

Radius of earth

\mathrm{ = 6}\mathrm{.4} \times \mathrm{1}{\mathrm{0}^\mathrm{6}}\mathrm{ }m,

Gravitational acceleration on earth

\mathrm{ = 10 }\,m{s^{ - 2}}]

View answer and explanation

Correct option: A

{10^4}\mathrm{ }K

Option A (

{10^4}\mathrm{ }K

) is correct because it is the temperature at which the root mean square velocity equals the escape velocity, calculated using the given constants.

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Assertion: The pressure exerted by an enclosed ideal gas does not depend on the shape of the container.
Reason: The pressure of an ideal gas depends on the number moles, temperature and volume of the enclosed If

c_s

is the velocity of sound in air and

c

is the rms velocity, then Four particles have velocities

1,0,2,3 \mathrm{~m} / \mathrm{s}

. The root mean square of the particles is (in

\mathrm{m} / \mathrm{s}

) The translational degrees of freedom

(f_t)

and rotational degrees of freedom

(f_r)

{CH}_4

molecule are: On any planet, the presence of atmosphere implies (

{C_{rms}} =

= root mean square velocity of molecules and

{V_e} =

escape velocity) At a given temperature, the pressure of an ideal gas of density

\rho

is proportional to