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NEET UG PHYSICS MCQ: KINETIC THEORY OF GASES

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The root mean square speed of smoke particles of mass 5×10−17 kg5 \times 10^{-17} \mathrm{~kg} in their Brownian motion in air at NTP is approximately. [Given k=1.38×10−23JK−1k=1.38 \times 10^{-23} \mathrm{JK}^{-1} ]
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Correct option: C
15 mm s−115 \mathrm{~mm} \mathrm{~s}{ }^{-1}
Option C (15 mm s−115 \mathrm{~mm} \mathrm{~s}{ }^{-1}) is correct because it's calculated using the formula for root mean square speed, vrms=3kTmv_{rms} = \sqrt{\frac{3kT}{m}}, with appropriate substitutions.

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The absolute zero is the temperature at which The internal energy (U)\left( U \right), pressure (p)\left( p \right) and volume (V)\left( V \right) of an ideal gas are related as U=3pV+4U = 3pV + 4. The gas is A monoatomic ideal gas is contained in a rigid container of volume VV with walls of total inner surface area AA, thickness xx and thermal conductivity KK. The gas is at an initial temperature T0T_0 and pressure P0P_0. If the pressure of the gas as a function of time if the temperature of the surrounding air is TsT_{\mathrm{s}} is T0T0[Ts−(Ts−T0)e−ZkA3xRt]\frac{T_0}{T_0}\left[T_s-\left(\mathrm{T}_s-T_0\right)_e \frac{-Z k A}{3 x R} t\right]. Find the value of zz. All temperatures are in absolute scale. Assertion: The change in air pressure effect the speed of sound.
Reason: The speed of sound in a gas is proportional to the square of pressure.
The rms speed of oxygen molecule in a vessel at particular temperature is (1+γ28)12v,\left(1+\frac{\gamma}{28}\right)^{\frac{1}{2}} v, where vv is the average speed of the molecule. The value of γ\gamma will be: (π=227)\left(\pi=\frac{22}{7}\right) For an ideal gas the instantaneous change in pressure pp with volume VV is given by the equation dpdV = −ap.\frac{{dp}}{{dV}}\, = \, - ap. If p = p0p\, = \,{p_0} at V = 0V\, = \,0 is the given boundary condition, then the maximum temperature one mole of gas can attain is (Here RR is the gas constant)
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