KE

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. 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. 1g H2 gas expand at STP to occupy double of its original volume. The work done during the process is(1) 260 cal(3) 130 cal26.(2) 180 cal(4) 270 cal

Q. One mole of an ideal diatomic gas undergoes a transition from $\text{A to B}$ along a path $\text{AB}$ as shown in the figure. The change in internal energy of the gas during the transition is:

1. $-12\text{kJ}$
2. $-20\text{kJ}$
3. $12\text{kJ}$
4. $20\text{kJ}$

Q. A gas is allowed to expand in a well insulated container against a cons†an t external pressure of 2.5 atm from an initial volume of 2.50 L to a final volume of 4.50L the change in internal energy δ U of the gas in joules will be

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. $2342\text{J}$
4. $1564\text{J}$

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

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

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. derive expression for kinetic energy of translation for one mole of gas and hence that for a molecule of gas .hence explain the kinetic interpretation of temperature

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

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

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

Q.

. In Vander Waals corrected gas equation (P + a / V²) (V – b) = n R T, where a and b are the constants. Calculate the dimensional formulae of a and b.

Q. Why is the work done by gas when it expands negative? Work done is pressure * change in volume. Since final volume is larger than initial volume, it should be positive na?

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

Q. The average kinetic energy of a molecule is

1. smaller than rms speed
2. greater than rms speed
3. equal to rms speed
4. greater than or equal to rms speed

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 translational kinetic energy of all the molecules of $1$ mole of Helium gas having a volume $V$ exerting a pressure $P$ is $1000\text{J}$. The total kinetic energy (in $\text{Joule}$) of all the molecules of $1$ mole of $N_2$ gas having the same volume $V$ and exerting a pressure $2P$ is :

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