KE

Q.

Give reason for the following observation:

The smell of hot sizzling food reaches you several metres away but to get the smell from cold food you have to go close

Q. A gas mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is

1. $14RT$
2. $13RT$
3. $15RT$
4. $11RT$

Q. A tank used for filling helium balloons has a volume of $0.3{\text{m}}^3$ and contains $2\text{mol}$ of helium gas at ${20}^{\circ }\text{C}$. Assuming that the helium behaves like an ideal gas, find the total translational kinetic energy of the molecules of the gas

1. $7.3\text{kJ}$
2. $10\text{kJ}$
3. $3.65\text{kJ}$
4. $2.4\text{kJ}$

Q. The variation of translational kinetic energy of one mole of a monoatomic gas with temperature is shown in the graph. Find $\tan \theta$.

1. $\frac{9R}{2}$
2. $R$
3. $\frac{7R}{2}$
4. $\frac{3R}{2}$

Q.

The pressure exerted by an ideal gas is numerically equal to_________ of the mean kinetic energy of translation per unit volume of the gas.

Q. The volume of gas at 0^°c and 700 mm of Hg pressure is 760 cc. The number of molecules present in this volume is :

Q. The translational kinetic energy of $1\text{mole}$ of an ideal gas at standard temperature is close to

1. $3403\text{J}$
2. $3000\text{J}$
3. $1564\text{J}$
4. $2342\text{J}$

Q. A container is filled with $20\text{mole}$ of an ideal diatomic gas at absolute temperature $T$. When heat is supplied to it, the temperature remain constant but $8\text{mole}$ of the gas disassociates into atoms. The heat energy supplied to the gas is

1. $7RT$
2. $6RT$
3. $4RT$
4. $5RT$

Q. The graph between $\frac{1}{\lambda }$ and stopping potential $\left(V\right)$ of three metals in an experiment of photo-electric effect is plotted as shown in the figure. The work function of metals $1,2,3$ are $W_1$, $W_2$ and $W_3$ respectively. Which of the following statement (s) is/are correct? [Here $\lambda$ is the wavelength of the incident ray]

1. Ratio of work function $W_1:W_2:W_3=1:2:4$
2. Ratio of work function $W_1:W_2:W_3=4:2:1$
3. $\tan \theta$ is directly propotional to $\frac{hc}{e}$, where $h$ is planck's constant and $c$ is the speed of light.
4. The violet colour light can eject photoelectrons from metals $2$ and $3$

Q. Pressure exerted by a perfect gas is equal to

1. mean kinetic energy of translation per unit volume
2. half of mean kinetic energy of translation per unit volume
3. one third of mean kinetic energy of translation per unit volume
4. two third of mean kinetic energy of translation per unit volume

Q.

Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:

${}^{12}\text{N}{\to }^{12}{\text{C}}^{\ast }+e^{+}+v$

${}^{12}{\text{C}}^{\ast }{\to }^{12}\text{C}+v\left(4.43\text{MeV}\right)$

Q. A gas is in equilibrium at $T$ kelvin. Mass of one molecule is $m$ and, its component of velocity in $x$ direction is $v_x$. The mean of its $v_x^2$ is represented by $\frac{nkT}{m}$. Find $n$.

Q. The translational kinetic energy of all the molecules of Helium having a volume $V$ exerting a pressure $P$ is $1000\text{J}$. The total kinetic energy (in $\text{Joule}$) of all the molecules of $N_2$ having the same volume $V$ and exerting a pressure $2P$ is

1. $4000\text{J}$
2. $3000\text{J}$
3. $2000\text{J}$
4. $1000\text{J}$

Q.

The figure shows pressure versus density graph for an ideal gas at two temperature $T_1$ and $T_2$:

1. None of these

2. $T_1>T_2$

3. $T_1=T_2$

4. $T_1<T_2$

Q. What is the average translational kinetic energy of a gas molecule at $500\text{K}$?

1. $1035\times {10}^{-23}\text{J}$
2. $750\times {10}^{-23}\text{J}$
3. $1725\times {10}^{-23}\text{J}$
4. $1150\times {10}^{-23}\text{J}$

Q. A box contains $N$ molecules of a perfect ideal gas at temperature $T_1$ and pressure $P_1$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is $P_2$ and new temperature is $T_2$, then

1. $P_2=P_1,T_2=T_1$
2. $P_2=P_1,T_2=\frac{T_1}{2}$
3. $P_2=2P_1,T_2=T_1$
4. $P_2=2P_1,T_2=\frac{T_1}{2}$

Q. From the following statements , regarding an ideal gas at any given temperature $T$, choose the correct alternative$\left(s\right)$

1. The coefficient of volume expansion at constant pressure is the same for all ideal gases
2. The average translational kinetic energy per molecule of oxygen gas is $3kT$, where $k$ being Boltzmann constant
3. The mean -free path of molecules increases with decrease in the pressure
4. In a gaseous mixture, the average translational kinetic energy of the molecules of each component is different.

Q. If $2$ moles of an ideal monoatomic gas at temperature $T_0$ is mixed with $4$ moles of another ideal monoatomic gas at temperature $2T_0$, then the temperature of the mixture is

1. $\frac{3}{2}{T}_0$
2. $\frac{4}{3}{T}_0$
3. $\frac{5}{4}{T}_0$
4. $\frac{5}{3}{T}_0$

Q.

The root mean speed of gas molecules

1. Is the same for all gases at the same temperature

2. Depends on the mass of the gas molecule and its temperature

3. Is independent of the density and pressure of the gas

4. Depends only on the temperature and volume of the gas

Q. The variation of translational kinetic energy of one mole of a monoatomic gas with temperature is shown in the graph. Find $\tan \theta$.

1. $\frac{9R}{2}$
2. $R$
3. $\frac{7R}{2}$
4. $\frac{3R}{2}$

Q. In an $\alpha -$ decay, the kinetic energy of$\alpha -$ particle is $48\text{MeV}$ and $Q$ value of the reaction is $50\text{MeV}$. The mass number of the mother nucleus is _____.
(Assume that daughter nucleus is in ground state)

Q. $N$ molecules of an ideal gas at temperature $T_1$ and pressure $P_1$ are contained in a closed box. The molecules in the box gets doubled, Keeping total kinetic energy same. If new pressure is $P_2$ and temperature is $T_2$, Then:

1. $P_2=P,T_2=T_1$
2. $P_2=P_1,T_2=\frac{T_1}{2}$
3. $P_2=2P_1.T_2=T_1$
4. $P_2=2P_1,T_2=\frac{T_1}{2}$

Q. Initially, the nucleus of $\text{Radium}-226$ is at rest. It decays by emitting an $\alpha -$ particle, and thus the nucleus of $\text{Radon}$ is created. The released energy during the decay is $4.87\text{MeV}$, which appears as the kinetic energy of the two resulted particles. The kinetic energy of $\alpha -$ particle & $\text{Radon}$ nucleus are respectively.
$[m_{\alpha }=4.002u,m_{\text{Rn}}=222.017u]$

1. $0.09\text{MeV},4.78\text{MeV}$
2. $4.78\text{MeV},0.09\text{MeV}$
3. $3.08\text{MeV},0.09\text{MeV}$
4. $3.68\text{MeV},1.09\text{MeV}$

Q. A gas occupies 150 cm3 at 57.find temperature of gas if volume triples at constant pressure

Q.

The pressure exerted by a perfect gas is equal to

1. $\frac{2}{3}$ of mean kinetic energy.

2. half of mean kinetic energy per unit volume.

3. mean kinetic energy per unit volume

4. $\frac{2}{3}$ of mean kinetic energy per unit volume.

Q. A cylinder of capacity $20\text{L}$ is filled with $H_2$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5\times {10}^5\text{J}$. The pressure of hydrogen in the cylinder is

1. $2\times {10}^6{\text{N/m}}^2$
2. $3\times {10}^6{\text{N/m}}^2$
3. $4\times {10}^6{\text{N/m}}^2$
4. $5\times {10}^6{\text{N/m}}^2$

Q. What should be the percentage increase in pressure for a 5 %decrease in volume of a gas at constant temperature.

Q. The variation of translational kinetic energy of one mole of a monoatomic gas with temperature is shown in the graph. Find $\tan \theta$.

1. $\frac{9R}{2}$
2. $\frac{7R}{2}$
3. $R$
4. $\frac{3R}{2}$

Q. A box contains $N$ molecules of a perfect gas at temperature $T_1$ and pressure $P_1$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is $P_2$ and temperature is $T_2$, then

1. $P_2=2P_1$, $T_2=T_1$
2. $P_2=P_1$, $T_2=\frac{T_1}{2}$
3. $P_2=2P_1$, $T_2=\frac{T_1}{2}$
4. $P_2=P_1$, $T_2=T_1$

Q. $N$ molecules of an ideal gas at temperature $T_1$ and pressure $P_1$ are contained in a closed box. The molecules in the box gets doubled, Keeping total kinetic energy same. If new pressure is $P_2$ and temperature is $T_2$, Then:

1. $P_2=P,T_2=T_1$
2. $P_2=P_1,T_2=\frac{T_1}{2}$
3. $P_2=2P_1.T_2=T_1$
4. $P_2=2P_1,T_2=\frac{T_1}{2}$