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Kinetic Theory
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The temperature of a gas is $-50^\circ C$. To what temperature the gas should be heated so that the rms speed is increased by 3 times?A 223 KB $669^\circ C$C $3295^\circ C$D 3097 K
As $v_{rms}\propto\sqrt{T}$, the key treats 'increased by 3 times' as $4v$, so $T_f=16T_i=3295^\circ C$.
$T_i=-50^\circ C=223\ K$ $v_{rms}\propto\sqrt{T}$ As $v_{rms}$ increased by 3 times, $(v_{rms})_f=4(v_{rms})_{initial}$ $T_f=16T_i=16\times223=3568\ K$ $T_f=(3568-273)^\circ C=3295^\circ C$ -
The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is :A $5.6\ m^3$B $5.6\times10^6\ m^3$C $5.6\times10^3\ m^3$D $5.6\times10^{-3}\ m^3$
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Match Column-I and Column-II and choose the correct match from the given choices.
Column I
- A. Root mean square speed of gas molecules
- B. Pressure exerted by ideal gas
- C. Average kinetic energy of a molecules
- D. Total internal energy of 1 mole of a diatomic gas
Column II
- P. $\frac{1}{3}nm\bar{v}^2$
- Q. $\sqrt{\frac{3RT}{M}}$
- R. $\frac{5}{2}RT$
- S. $\frac{3}{2}k_BT$
Correct answer: A → Q, B → P, C → S, D → R
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The average thermal energy for a mono-atomic gas is: ($k_B$ is Boltzmann constant and $T$, absolute temperature)A $\frac{3}{2}k_BT$B $\frac{5}{2}k_BT$C $\frac{7}{2}k_BT$D $\frac{1}{2}k_BT$
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The mean free path for a gas, with molecular diameter $d$ and number density $n$ can be expressed as:A $\frac{1}{\sqrt{2}\,n\pi d^2}$B $\frac{1}{\sqrt{2}\,n^2\pi d^2}$C $\frac{1}{\sqrt{2}\,n^2\pi^2d^2}$D $\frac{1}{\sqrt{2}\,n\pi d}$
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A cylinder contains hydrogen gas at pressure of 249 kPa and temperature $27^\circ C$. Its density is: ($R=8.3\ J\,mol^{-1}K^{-1}$)A $0.2\ kg/m^3$B $0.1\ kg/m^3$C $0.02\ kg/m^3$D $0.5\ kg/m^3$
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Increase in temperature of a gas filled in a container would lead to:A increase in its massB increase in its kinetic energyC decrease in its pressureD decrease in intermolecular distance