Ideal Gas Equation

Q. The unit cell length of NaCl crystal is 564 pm. Its density would be(2) 2.165 g/cm3TR(4) 4.33 g/cm(1) 1.082 g/cm3(3) 3.247 gm/cm3

Q. An ideal gas undergoes four different processes from the same initial state (Fig.). Four processes are adiabatic, isothermal, isobaric and isochoric. Out of 1, 2, 3 and 4 which one is adiabatic.

1. 2
2. 3
3. 1
4. 4

Q.

During an experiment, an ideal gas is found to obey an additional law $p{V}^2$ = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.

Q. Increase in temperature of a gas filled in a container would lead to

1. increase in its mass.
2. increase in its kinetic energy.
3. decrease in its pressure.
4. decrease in intermolecular distance.

Q. Ratio of rotational kinetic energy to the total energy for diatomic gas molecule at room temperature is

1. $5:2$
2. $2:5$
3. $3:2$
4. $2:3$

Q. What is the dimension of the physical quantity$\left(\alpha \right)$ in the equation, $P=\frac{\text{density}}{\alpha }$, where $P$ is the pressure ?

1. ${\text{L}}^{-2}{\text{T}}^2$
2. $\text{M}{\text{L}}^4{\text{T}}^{-2}$
3. $\text{M}{\text{L}}^2{\text{T}}^{-1}$
4. ${\text{L}}^{-3}{\text{T}}^2$

Q. Two gases $A$ and $B$ having same pressure $P$, volume $V$ and temperature $T$ are mixed. If the mixture has volume and temperature as $V$ and $T$ respectively, then the pressure of the mixture will be

1. $4P$
2. $3P$
3. $2P$
4. $P$

Q. Two nuclei have mass numbers in the ratio 27:125. what is the ratio of their nuclear densities?

Q. The graph between log(x/m) vs log P is straight line inclined at an angle 45 with intercept 0.30. What will be rate of adsorption at pressure 0.4atm?

Q. A short electric dipole is placed on the axis of a uniformly charged ring of Radius R so that its dipole moment is along the axis. if the net force on the dipole is zero the dis†an ce of the dipole from the centre of the ring is

Q.

How do you find density in ideal gas law?

Q.

What is the value of molar volume of a gas at $STP$?

Q. The lowest pressure (the best vaccum) that can be created in laboratory at ${20}^{\circ }\text{C}$ is ${10}^{-10}\text{mm}$ of $\text{Hg}$. At this pressure, the number of ideal gas molecules per ${\text{cm}}^3$ will be

1. $3.22\times {10}^{12}$
2. $1.61\times {10}^{10}$
3. $3.22\times {10}^8$
4. $3.29\times {10}^6$

Q. A vessel is filled with an ideal gas at a pressure of $10\text{atm}$ and temperature of $27{}^{\circ }\text{C}$. Half of the mass is removed from the vessel and temperature of the remaining gas is increased to $87{}^{\circ }\text{C}$. Then the pressure of the gas in the vessel will be

1. $5\text{atm}$
2. $6\text{atm}$
3. $7\text{atm}$
4. $8\text{atm}$

Q.

What are the three principles of kinetic theory?

Q.

What is the kinetic theory of Ideal gas?

Q.

Find the number of molecules of an ideal gas in a volume of 1000 $c{m}^3$ at STP.

Q. In an experiment on the specific heat of a metal, a $0.20\text{kg}$ block of the metal at ${150}^{\circ }C$ is dropped in a copper calorimeter (of water equivalent $0.025\text{kg}$) containing $150c{m}^3$ of water at ${27}^{\circ }C$. The final temperature is ${40}^{\circ }C$. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater of smaller than the actual value for specific heat of the metal.

Q. A vessel has $6\text{g}$ of hydrogen at pressure $P$ and temperature $500\text{K}$. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $P/2$ and temperature falls to $300\text{K}$?

1. $2\text{g}$
2. $1\text{g}$
3. $4\text{g}$
4. $3\text{g}$

Q. One mole of an ideal gas at a temperature $T_{1}K$ expands slowly according to the law $\frac{p}{v}=$ constant. It final temperature is $T_{2}K$. The work done by the gas is

1. $\frac{R}{2}(T_2-T_1)$
2. $2R(T_2-T_1)$
3. $R(T_2-T_1)$
4. $\frac{2R}{3}(T_2-T_1)$

Q. Two balloons are filled, one with pure $He$ gas and other by air. If the pressure and temperature of these balloons are same, then the number of molecules per unit volume is:

1. more in the $He$ filled balloon.
2. more in the air filled balloon.
3. same in both the balloons.
4. in the ratio of $1:4$.

Q. A cylinder contained 10 kg of gas at pressure ${10}^{7}N/m^2.$ The quantity of gas taken out of cylinder if final pressure is $2.5\times {10}^{6}M/m$ is (assume the temperature of gas is constant)

1. Zero
2. 7.5 kg
3. 5 kg
4. 2.5 kg

Q. The manometric head of a pump is

1. The difference in elevation between the water surface in the high level reservoir and the water level in the sump
2. The height to which water is lifted by the pump measured above the pump centreline
3. The difference in Piezometric heads between the points on the delivery and suction pipes as close to the pump as possible
4. The head developed by the pump

Q. Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainity in determining the position of an electron to that of a proton is proportional to

1. $\frac{m_p}{m_e}$
2. $\sqrt{\frac{m_p}{m_e}}$
3. $\sqrt{\frac{m_e}{m_p}}$
4. ${\left[\frac{m_e}{m_p}\right]}^{\frac{3}{2}}$

Q. In the process $PV=$ constant, pressure $\left(P\right)$ versus density $\left(\rho \right)$, graph of an ideal gas is:

1. a straight line parallel to $P-$ axis
2. a straight line parallel to $\rho -$ axis
3. an inclined straight line passing through the origin
4. a parabola

Q. One litre of oxygen at a pressure of $1\text{atm}$ and two litres of nitrogen at a pressure of $0.5\text{atm}$ at the same temperature are introduced into a vessel of one litre volume. If there is no change in the temperature, then final pressure of the mixture of gases is

1. $1\text{atm}$
2. $3\text{atm}$
3. $2\text{atm}$
4. $4\text{atm}$

Q.

Two thermally insulated vessels 1 and 2 are filled with air at temperatures $(T_1,T_2)$, volume $(V_1,V_2)$ and pressure $(P_1,P_2)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

1. $T_1+T_2$
   

2. $T_1{T}_2(P_1{V}_1+P_2{V}_2)/(P_1{V}_1{T}_2+P_2{V}_2{T}_1)$
   

3. $T_1{T}_2(P_1{V}_1+P_2{V}_2)/(P_1{V}_1{T}_1+P_2{V}_2{T}_2)$

4. $(T_1+T_2)/2$
   

Q. At $0^{\circ }C$ pressure measured by barometer is 760 mm. What will be pressure at ${100}^{\circ }C$

1. 760 mm
2. 730 mm
3. 780 mm
4. None of these

Q.

Find the number of molecules in 1 $c{m}^3$ of an ideal gas at $0^0$'C' and at a pressure of ${10}^{-5}$ mm of mercury.

Q.

A solid sphere and a hollow sphere of the same mass have the same M.I. about their respective diameters the ratio of their radii will be.