Ideal Gas Equation and Vander Waal equation
Kinetic Theory of Gases

139030 An air bubble of volume $v_{0}$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density) of water is $\rho$

1 $v_{0}$
2 $\mathrm{v}_{0}(\rho \mathrm{gh} / \mathrm{p})$
3 $\frac{\mathrm{v}_{0}}{\left(1+\frac{\rho g h}{\mathrm{p}}\right)}$
4 $\mathrm{v}_{0}\left(1+\frac{\rho \mathrm{gh}}{\mathrm{p}}\right)$
Kinetic Theory of Gases

139031 A vessel containing 1 mole of $\mathrm{O}_{2}$ gas (molar mass 32) at temperature $T$. The pressure of the gas is $P$. An identical vessel containing one mole of the gas (molar mass 4) at temperature $2 \mathrm{~T}$ has a pressure of

1 $\mathrm{P} / 8$
2 $\mathrm{P}$
3 $2 \mathrm{P}$
4 $8 \mathrm{P}$
Kinetic Theory of Gases

139032 0.5 mole of an ideal gas at constant temperature $27^{\circ} \mathrm{C}$ kept inside a cylinder of length $L$ and cross-section area $A$ closed by a massless piston.

The cylinder is attached with a conducting rod of length $L$, cross-section area $(1 / 9) \mathrm{m}^{2}$ and thermal conductivity $k$, whose other end is maintained at $0^{\circ} \mathrm{C}$. If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height $L / 2$ from the bottom of cylinder is : [Neglect any kind of heat loss from system]

1 $\left(\frac{\mathrm{k}}{\mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
2 $\left(\frac{\mathrm{k}}{10 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
3 $\left(\frac{\mathrm{k}}{100 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
4 $\left(\frac{\mathrm{k}}{1000 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
Kinetic Theory of Gases

139035 If the volume of the gas containing $n$ number of molecules is $\mathrm{V}$, then the pressure will decrease due to force of intermolecular attraction in the proportion

1 $n / V$
2 $n / V^{2}$
3 $(\mathrm{n} / \mathrm{V})^{2}$
4 $1 / V^{2}$
Kinetic Theory of Gases

139030 An air bubble of volume $v_{0}$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density) of water is $\rho$

1 $v_{0}$
2 $\mathrm{v}_{0}(\rho \mathrm{gh} / \mathrm{p})$
3 $\frac{\mathrm{v}_{0}}{\left(1+\frac{\rho g h}{\mathrm{p}}\right)}$
4 $\mathrm{v}_{0}\left(1+\frac{\rho \mathrm{gh}}{\mathrm{p}}\right)$
Kinetic Theory of Gases

139031 A vessel containing 1 mole of $\mathrm{O}_{2}$ gas (molar mass 32) at temperature $T$. The pressure of the gas is $P$. An identical vessel containing one mole of the gas (molar mass 4) at temperature $2 \mathrm{~T}$ has a pressure of

1 $\mathrm{P} / 8$
2 $\mathrm{P}$
3 $2 \mathrm{P}$
4 $8 \mathrm{P}$
Kinetic Theory of Gases

139032 0.5 mole of an ideal gas at constant temperature $27^{\circ} \mathrm{C}$ kept inside a cylinder of length $L$ and cross-section area $A$ closed by a massless piston.

The cylinder is attached with a conducting rod of length $L$, cross-section area $(1 / 9) \mathrm{m}^{2}$ and thermal conductivity $k$, whose other end is maintained at $0^{\circ} \mathrm{C}$. If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height $L / 2$ from the bottom of cylinder is : [Neglect any kind of heat loss from system]

1 $\left(\frac{\mathrm{k}}{\mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
2 $\left(\frac{\mathrm{k}}{10 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
3 $\left(\frac{\mathrm{k}}{100 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
4 $\left(\frac{\mathrm{k}}{1000 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
Kinetic Theory of Gases

139035 If the volume of the gas containing $n$ number of molecules is $\mathrm{V}$, then the pressure will decrease due to force of intermolecular attraction in the proportion

1 $n / V$
2 $n / V^{2}$
3 $(\mathrm{n} / \mathrm{V})^{2}$
4 $1 / V^{2}$
Kinetic Theory of Gases

139030 An air bubble of volume $v_{0}$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density) of water is $\rho$

1 $v_{0}$
2 $\mathrm{v}_{0}(\rho \mathrm{gh} / \mathrm{p})$
3 $\frac{\mathrm{v}_{0}}{\left(1+\frac{\rho g h}{\mathrm{p}}\right)}$
4 $\mathrm{v}_{0}\left(1+\frac{\rho \mathrm{gh}}{\mathrm{p}}\right)$
Kinetic Theory of Gases

139031 A vessel containing 1 mole of $\mathrm{O}_{2}$ gas (molar mass 32) at temperature $T$. The pressure of the gas is $P$. An identical vessel containing one mole of the gas (molar mass 4) at temperature $2 \mathrm{~T}$ has a pressure of

1 $\mathrm{P} / 8$
2 $\mathrm{P}$
3 $2 \mathrm{P}$
4 $8 \mathrm{P}$
Kinetic Theory of Gases

139032 0.5 mole of an ideal gas at constant temperature $27^{\circ} \mathrm{C}$ kept inside a cylinder of length $L$ and cross-section area $A$ closed by a massless piston.

The cylinder is attached with a conducting rod of length $L$, cross-section area $(1 / 9) \mathrm{m}^{2}$ and thermal conductivity $k$, whose other end is maintained at $0^{\circ} \mathrm{C}$. If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height $L / 2$ from the bottom of cylinder is : [Neglect any kind of heat loss from system]

1 $\left(\frac{\mathrm{k}}{\mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
2 $\left(\frac{\mathrm{k}}{10 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
3 $\left(\frac{\mathrm{k}}{100 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
4 $\left(\frac{\mathrm{k}}{1000 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
Kinetic Theory of Gases

139035 If the volume of the gas containing $n$ number of molecules is $\mathrm{V}$, then the pressure will decrease due to force of intermolecular attraction in the proportion

1 $n / V$
2 $n / V^{2}$
3 $(\mathrm{n} / \mathrm{V})^{2}$
4 $1 / V^{2}$
Kinetic Theory of Gases

139030 An air bubble of volume $v_{0}$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density) of water is $\rho$

1 $v_{0}$
2 $\mathrm{v}_{0}(\rho \mathrm{gh} / \mathrm{p})$
3 $\frac{\mathrm{v}_{0}}{\left(1+\frac{\rho g h}{\mathrm{p}}\right)}$
4 $\mathrm{v}_{0}\left(1+\frac{\rho \mathrm{gh}}{\mathrm{p}}\right)$
Kinetic Theory of Gases

139031 A vessel containing 1 mole of $\mathrm{O}_{2}$ gas (molar mass 32) at temperature $T$. The pressure of the gas is $P$. An identical vessel containing one mole of the gas (molar mass 4) at temperature $2 \mathrm{~T}$ has a pressure of

1 $\mathrm{P} / 8$
2 $\mathrm{P}$
3 $2 \mathrm{P}$
4 $8 \mathrm{P}$
Kinetic Theory of Gases

139032 0.5 mole of an ideal gas at constant temperature $27^{\circ} \mathrm{C}$ kept inside a cylinder of length $L$ and cross-section area $A$ closed by a massless piston.

The cylinder is attached with a conducting rod of length $L$, cross-section area $(1 / 9) \mathrm{m}^{2}$ and thermal conductivity $k$, whose other end is maintained at $0^{\circ} \mathrm{C}$. If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height $L / 2$ from the bottom of cylinder is : [Neglect any kind of heat loss from system]

1 $\left(\frac{\mathrm{k}}{\mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
2 $\left(\frac{\mathrm{k}}{10 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
3 $\left(\frac{\mathrm{k}}{100 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
4 $\left(\frac{\mathrm{k}}{1000 \mathrm{R}}\right) \mathrm{m} / \mathrm{sec}$
Kinetic Theory of Gases

139035 If the volume of the gas containing $n$ number of molecules is $\mathrm{V}$, then the pressure will decrease due to force of intermolecular attraction in the proportion

1 $n / V$
2 $n / V^{2}$
3 $(\mathrm{n} / \mathrm{V})^{2}$
4 $1 / V^{2}$